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トリオ数列

トリオ数列数の定義

A=9:dim B[∞],C[∞],D[∞],E[∞],F[∞]
for G=0 to 9
 for H=0 to A
  B[H]=H:C[H]=H:D[H]=H
 next
 E[1]=1:F[1]=1
 for I=A to 0 step -1
  A=A*A
  for J=0 to I
   if B[I-J]<B[I]-K | B[I]=0 then
    if 0<C[I] then K=B[I]-B[I-J]
    if C[I-J]<C[I]-L | C[I]=0 then
     if 0<D[I] then L=C[I]-C[I-J]
     if D[I-J]<D[I] | D[I]=0 then M=J:J=I
    endif
   endif
  next
  for N=1 to M
   for O=N to 0 step -1
    if B[I-M+O]<B[I-M+N] then
     if B[I-M]<B[I-M+O] & E[O+1]=1 then E[N+1]=1 else E[N+1]=0
     if C[I-M]<C[I-M+O] & F[O+1]=1 then F[N+1]=1 else F[N+1]=0
     O=0
    endif
   next
  next
  for P=1 to A
   for Q=1 to M
    B[I]=B[I-M]:C[I]=C[I-M]:D[I]=D[I-M]
    if E[Q]=1 then B[I]=B[I]+K
    if F[Q]=1 then C[I]=C[I]+L
    I=I+1
   next
  next
  K=0:L=0
 next
next
print A

解析

\begin{array}{ll} (0,0,0)&=&1\\ (0,0,0)(0,0,0)&=&2\\ (0,0,0)(0,0,0)(0,0,0)&=&3\\ (0,0,0)(1,0,0)&=&\omega\\ (0,0,0)(1,0,0)(0,0,0)&=&\omega+1\\ (0,0,0)(1,0,0)(0,0,0)(1,0,0)&=&\omega+\omega\\ (0,0,0)(1,0,0)(0,0,0)(1,0,0)(0,0,0)(1,0,0)&=&\omega\cdot3\\ (0,0,0)(1,0,0)(1,0,0)&=&\omega\cdot\omega\\ (0,0,0)(1,0,0)(1,0,0)(0,0,0)&=&\omega\cdot\omega+1\\ (0,0,0)(1,0,0)(1,0,0)(0,0,0)(1,0,0)(1,0,0)&=&(\omega\cdot\omega)\cdot2\\ (0,0,0)(1,0,0)(1,0,0)(1,0,0)&=&\omega^2\cdot\omega\\ (0,0,0)(1,0,0)(1,0,0)(1,0,0)(1,0,0)&=&\omega^4\\ (0,0,0)(1,0,0)(2,0,0)&=&\omega^\omega\\ (0,0,0)(1,0,0)(2,0,0)(1,0,0)&=&\omega^{\omega+1}\\ (0,0,0)(1,0,0)(2,0,0)(1,0,0)(2,0,0)&=&\omega^{\omega\cdot2}\\ (0,0,0)(1,0,0)(2,0,0)(2,0,0)&=&\omega^{\omega^2}\\ (0,0,0)(1,0,0)(2,0,0)(3,0,0)&=&\omega^{\omega^\omega}\\ (0,0,0)(1,0,0)(2,0,0)(3,0,0)(4,0,0)&=&\omega^{\omega^{\omega^\omega}}\\ (0,0,0)(1,1,0)&=&\psi_\Omega(0)\\ (0,0,0)(1,1,0)(1,0,0)(0,0,0)(1,1,0)(1,0,0)&=&\psi_\Omega(0)\cdot2\\ (0,0,0)(1,1,0)(1,0,0)&=&\psi_\Omega(0)\cdot\omega\\ (0,0,0)(1,1,0)(1,0,0)(1,0,0)&=&\psi_\Omega(0)\cdot\omega^2\\ (0,0,0)(1,1,0)(1,0,0)(2,0,0)&=&\psi_\Omega(0)\cdot\omega^\omega\\ (0,0,0)(1,1,0)(1,0,0)(2,0,0)(3,0,0)&=&\psi_\Omega(0)\cdot\omega^{\omega^\omega}\\ (0,0,0)(1,1,0)(1,0,0)(2,1,0)&=&\psi_\Omega(0)\cdot\psi_\Omega(0)\\ (0,0,0)(1,1,0)(1,0,0)(2,1,0)(1,0,0)(2,1,0)&=&\psi_\Omega(0)^2\cdot\psi_\Omega(0)\\ (0,0,0)(1,1,0)(1,0,0)(2,1,0)(1,0,0)(2,1,0)\\ (1,0,0)(2,1,0)&=&\psi_\Omega(0)^4\\ (0,0,0)(1,1,0)(1,0,0)(2,1,0)(2,0,0)&=&\psi_\Omega(0)^\omega\\ (0,0,0)(1,1,0)(1,0,0)(2,1,0)(2,0,0)(1,0,0)\\ (2,1,0)&=&\psi_\Omega(0)^{\omega+1}\\ (0,0,0)(1,1,0)(1,0,0)(2,1,0)(2,0,0)(1,0,0)\\ (2,1,0)(2,0,0)&=&\psi_\Omega(0)^{\omega\cdot2}\\ (0,0,0)(1,1,0)(1,0,0)(2,1,0)(2,0,0)(2,0,0)&=&\psi_\Omega(0)^{\omega^2}\\ (0,0,0)(1,1,0)(1,0,0)(2,1,0)(2,0,0)(3,0,0)&=&\psi_\Omega(0)^{\omega^\omega}\\ (0,0,0)(1,1,0)(1,0,0)(2,1,0)(2,0,0)(3,0,0)\\ (4,0,0)&=&\psi_\Omega(0)^{\omega^{\omega^\omega}}\\ (0,0,0)(1,1,0)(1,0,0)(2,1,0)(2,0,0)(3,1,0)&=&\psi_\Omega(0)^{\psi_\Omega(0)}\\ (0,0,0)(1,1,0)(1,0,0)(2,1,0)(2,0,0)(3,1,0)\\ (3,0,0)(4,1,0)&=&\psi_\Omega(0)^{\psi_\Omega(0)^2}\\ (0,0,0)(1,1,0)(1,0,0)(2,1,0)(2,0,0)(3,1,0)\\ (3,0,0)(4,1,0)(4,0,0)(5,1,0)&=&\psi_\Omega(0)^{\psi_\Omega(0)^{\psi_\Omega(0)}}\\ (0,0,0)(1,1,0)(1,1,0)&=&\psi_\Omega(1)\\ (0,0,0)(1,1,0)(1,1,0)(1,0,0)&=&\psi_\Omega(1)\cdot\omega\\ (0,0,0)(1,1,0)(1,1,0)(1,0,0)(2,1,0)&=&\psi_\Omega(1)\cdot\psi_\Omega(0)\\ (0,0,0)(1,1,0)(1,1,0)(1,0,0)(2,1,0)(2,1,0)&=&\psi_\Omega(1)^2\\ (0,0,0)(1,1,0)(1,1,0)(1,0,0)(2,1,0)(2,1,0)\\ (2,0,0)&=&\psi_\Omega(1)^\omega\\ (0,0,0)(1,1,0)(1,1,0)(1,0,0)(2,1,0)(2,1,0)\\ (2,0,0)(3,1,0)&=&\psi_\Omega(1)^{\psi_\Omega(0)}\\ (0,0,0)(1,1,0)(1,1,0)(1,0,0)(2,1,0)(2,1,0)\\ (2,0,0)(3,1,0)(3,1,0)&=&\psi_\Omega(1)^{\psi_\Omega(1)}\\ (0,0,0)(1,1,0)(1,1,0)(1,0,0)(2,1,0)(2,1,0)\\ (2,0,0)(3,1,0)(3,1,0)(3,0,0)(4,1,0)(4,1,0)&=&\psi_\Omega(1)^{\psi_\Omega(1)^2}\\ (0,0,0)(1,1,0)(1,1,0)(1,0,0)(2,1,0)(2,1,0)\\ (2,0,0)(3,1,0)(3,1,0)(3,0,0)(4,1,0)(4,1,0)\\ (4,0,0)(5,1,0)(5,1,0)&=&\psi_\Omega(1)^{\psi_\Omega(1)^{\psi_\Omega(1)}}\\ (0,0,0)(1,1,0)(1,1,0)(1,1,0)&=&\psi_\Omega(2)\\ (0,0,0)(1,1,0)(1,1,0)(1,1,0)(1,1,0)&=&\psi_\Omega(3)\\ (0,0,0)(1,1,0)(2,0,0)&=&\psi_\Omega(\omega)\\ (0,0,0)(1,1,0)(2,0,0)(1,1,0)&=&\psi_\Omega(\omega+1)\\ (0,0,0)(1,1,0)(2,0,0)(1,1,0)(2,0,0)&=&\psi_\Omega(\omega\cdot2)\\ (0,0,0)(1,1,0)(2,0,0)(2,0,0)&=&\psi_\Omega(\omega^2)\\ (0,0,0)(1,1,0)(2,0,0)(3,0,0)&=&\psi_\Omega(\omega^\omega)\\ (0,0,0)(1,1,0)(2,0,0)(3,1,0)&=&\psi_\Omega(\psi_\Omega(0))\\ (0,0,0)(1,1,0)(2,0,0)(3,1,0)(4,0,0)(5,1,0)&=&\psi_\Omega(\psi_\Omega(\psi_\Omega(0)))\\ (0,0,0)(1,1,0)(2,1,0)&=&\psi_\Omega(\Omega)\\ (0,0,0)(1,1,0)(2,1,0)(1,1,0)&=&\psi_\Omega(\Omega+1)\\ (0,0,0)(1,1,0)(2,1,0)(1,1,0)(2,0,0)&=&\psi_\Omega(\Omega+\omega)\\ (0,0,0)(1,1,0)(2,1,0)(1,1,0)(2,0,0)(3,1,0)&=&\psi_\Omega(\Omega+\psi_\Omega(0))\\ (0,0,0)(1,1,0)(2,1,0)(1,1,0)(2,0,0)(3,1,0)\\ (4,1,0)&=&\psi_\Omega(\Omega+\psi_\Omega(\Omega))\\ (0,0,0)(1,1,0)(2,1,0)(1,1,0)(2,0,0)(3,1,0)\\ (4,1,0)(3,1,0)(4,0,0)(5,1,0)(6,1,0)&=&\psi_\Omega(\Omega+\psi_\Omega(\Omega+\psi_\Omega(\Omega)))\\ (0,0,0)(1,1,0)(2,1,0)(1,1,0)(2,1,0)&=&\psi_\Omega(\Omega+\Omega)\\ (0,0,0)(1,1,0)(2,1,0)(1,1,0)(2,1,0)(1,1,0)\\ (2,1,0)&=&\psi_\Omega(\Omega\cdot3)\\ (0,0,0)(1,1,0)(2,1,0)(2,0,0)&=&\psi_\Omega(\Omega\cdot\omega)\\ (0,0,0)(1,1,0)(2,1,0)(2,0,0)(3,1,0)&=&\psi_\Omega(\Omega\cdot\psi_\Omega(0))\\ (0,0,0)(1,1,0)(2,1,0)(2,0,0)(3,1,0)(4,1,0)&=&\psi_\Omega(\Omega\cdot\psi_\Omega(\Omega))\\ (0,0,0)(1,1,0)(2,1,0)(2,0,0)(3,1,0)(4,1,0)\\ (4,0,0)(5,1,0)(6,1,0)&=&\psi_\Omega(\Omega\cdot\psi_\Omega(\Omega\cdot\psi_\Omega(\Omega)))\\ (0,0,0)(1,1,0)(2,1,0)(2,1,0)&=&\psi_\Omega(\Omega\cdot\Omega)\\ (0,0,0)(1,1,0)(2,1,0)(2,1,0)(2,0,0)&=&\psi_\Omega(\Omega^2\cdot\omega)\\ (0,0,0)(1,1,0)(2,1,0)(2,1,0)(2,1,0)&=&\psi_\Omega(\Omega^3)\\ (0,0,0)(1,1,0)(2,1,0)(3,0,0)&=&\psi_\Omega(\Omega^\omega)\\ (0,0,0)(1,1,0)(2,1,0)(3,0,0)(4,1,0)&=&\psi_\Omega(\Omega^{\psi_\Omega(0)})\\ (0,0,0)(1,1,0)(2,1,0)(3,0,0)(4,1,0)(5,1,0)&=&\psi_\Omega(\Omega^{\psi_\Omega(\Omega)})\\ (0,0,0)(1,1,0)(2,1,0)(3,0,0)(4,1,0)(5,1,0)\\ (6,0,0)(7,1,0)(8,1,0)&=&\psi_\Omega(\Omega^{\psi_\Omega(\Omega^{\psi_\Omega(\Omega)})})\\ (0,0,0)(1,1,0)(2,1,0)(3,1,0)&=&\psi_\Omega(\Omega^\Omega)\\ (0,0,0)(1,1,0)(2,1,0)(3,1,0)(4,1,0)&=&\psi_\Omega(\Omega^{\Omega^2})\\ (0,0,0)(1,1,0)(2,1,0)(3,1,0)(4,1,0)(5,1,0)&=&\psi_\Omega(\Omega^{\Omega^\Omega})\\ (0,0,0)(1,1,0)(2,2,0)&=&\psi_\Omega(\psi_{\Omega_2}(0))\\ (0,0,0)(1,1,0)(2,2,0)(1,1,0)&=&\psi_\Omega(\psi_{\Omega_2}(0)+1)\\ (0,0,0)(1,1,0)(2,2,0)(1,1,0)(2,2,0)&=&\psi_\Omega(\psi_{\Omega_2}(0)\cdot2)\\ (0,0,0)(1,1,0)(2,2,0)(2,1,0)(3,2,0)&=&\psi_\Omega(\psi_{\Omega_2}(0)^2)\\ (0,0,0)(1,1,0)(2,2,0)(2,1,0)(3,2,0)(3,1,0)\\ (4,2,0)&=&\psi_\Omega(\psi_{\Omega_2}(0)^{\psi_{\Omega_2}(0)})\\ (0,0,0)(1,1,0)(2,2,0)(2,1,0)&=&\psi_\Omega(\psi_{\Omega_2}(1))\\ (0,0,0)(1,1,0)(2,2,0)(3,1,0)&=&\psi_\Omega(\psi_{\Omega_2}(\Omega))\\ (0,0,0)(1,1,0)(2,2,0)(3,1,0)(4,2,0)&=&\psi_\Omega(\psi_{\Omega_2}(\psi_{\Omega_2}(0)))\\ (0,0,0)(1,1,0)(2,2,0)(3,2,0)&=&\psi_\Omega(\psi_{\Omega_2}(\Omega_2))\\ (0,0,0)(1,1,0)(2,2,0)(3,2,0)(2,2,0)&=&\psi_\Omega(\psi_{\Omega_2}(\Omega_2+1))\\ (0,0,0)(1,1,0)(2,2,0)(3,2,0)(2,2,0)(3,2,0)&=&\psi_\Omega(\psi_{\Omega_2}(\Omega_2\cdot2))\\ (0,0,0)(1,1,0)(2,2,0)(3,2,0)(3,2,0)&=&\psi_\Omega(\psi_{\Omega_2}(\Omega_2^2))\\ (0,0,0)(1,1,0)(2,2,0)(3,2,0)(4,2,0)&=&\psi_\Omega(\psi_{\Omega_2}(\Omega_2^{\Omega_2}))\\ (0,0,0)(1,1,0)(2,2,0)(3,3,0)&=&\psi_\Omega(\psi_{\Omega_2}(\psi_{\Omega_3}(0)))\\ (0,0,0)(1,1,0)(2,2,0)(3,3,0)(4,4,0)&=&\psi_\Omega(\psi_{\Omega_2}(\psi_{\Omega_3}(\psi_{\Omega_4}(0))))\\ (0,0,0)(1,1,1)&=&\psi_\Omega(\Omega_\omega)\\ &=&\psi(\psi_\omega(0))\\ (0,0,0)(1,1,1)(1,1,0)&=&\psi_\Omega(\Omega_\omega+1)\\ (0,0,0)(1,1,1)(1,1,0)(2,2,0)&=&\psi_\Omega(\Omega_\omega+\psi_{\Omega_2}(0))\\ (0,0,0)(1,1,1)(1,1,0)(2,2,0)(3,3,0)&=&\psi_\Omega(\Omega_\omega+\psi_{\Omega_2}(\psi_{\Omega_3}(0)))\\ (0,0,0)(1,1,1)(1,1,0)(2,2,1)&=&\psi_\Omega(\Omega_\omega+\psi_{\Omega_2}(\Omega_\omega))\\ (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)&=&\psi_\Omega(\Omega_\omega+\psi_{\Omega_2}(\Omega_\omega+1))\\ (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,3,0)&=&\psi_\Omega(\Omega_\omega+\psi_{\Omega_2}(\Omega_\omega+\psi_{\Omega_3}(0)))\\ (0,0,0)(1,1,1)(1,1,0)(2,2,1)(2,2,0)(3,3,1)&=&\psi_\Omega(\Omega_\omega+\psi_{\Omega_2}(\Omega_\omega+\psi_{\Omega_3}(\Omega_\omega)))\\ (0,0,0)(1,1,1)(1,1,1)&=&\psi_\Omega(\Omega_\omega+\Omega_\omega)\\ (0,0,0)(1,1,1)(1,1,1)(1,1,1)&=&\psi_\Omega(\Omega_\omega\cdot3)\\ (0,0,0)(1,1,1)(2,0,0)&=&\psi_\Omega(\Omega_\omega\cdot\omega)\\ (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,1,0)(3,1,0)&=&\psi_\Omega(\Omega_\omega\cdot\omega+\Omega^\Omega)\\ (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)&=&\psi_\Omega(\Omega_\omega\cdot\omega+\psi_{\Omega_2}(\Omega_\omega\cdot\omega))\\ (0,0,0)(1,1,1)(2,0,0)(1,1,0)(2,2,1)(3,0,0)\\ (3,3,0)(4,4,1)(5,0,0)&=&\psi_\Omega(\Omega_\omega\cdot\omega+\psi_{\Omega_2}(\Omega_\omega\cdot\omega+\psi_{\Omega_3}(\Omega_\omega\cdot\omega)))\\ (0,0,0)(1,1,1)(2,0,0)(1,1,1)&=&\psi_\Omega(\Omega_\omega\cdot\omega+\Omega_\omega )\\ (0,0,0)(1,1,1)(2,0,0)(3,1,0)&=&\psi_\Omega(\Omega_\omega\cdot\psi_{\Omega}(0))\\ (0,0,0)(1,1,1)(2,0,0)(3,1,0)(1,1,0)(2,2,1)\\ (3,0,0)(4,1,0)&=&\psi_\Omega(\Omega_\omega\cdot\psi_{\Omega}(0)+\psi_{\Omega_2}(\Omega_\omega\cdot\psi_{\Omega}(0)))\\ (0,0,0)(1,1,1)(2,0,0)(3,1,0)(1,1,1)&=&\psi_\Omega(\Omega_\omega\cdot\psi_{\Omega}(0)+\Omega_\omega)\\ (0,0,0)(1,1,1)(2,1,0)&=&\psi_\Omega(\Omega_\omega\cdot\Omega)\\ (0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)&=&\psi_\Omega(\Omega_\omega\cdot\Omega+\psi_{\Omega_2}(\Omega_\omega\cdot\Omega))\\ (0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)\\ (2,2,0)(3,3,1)(4,1,0)&=&\psi_\Omega(\Omega_\omega\cdot\Omega+\psi_{\Omega_2}(\Omega_\omega\cdot\Omega+\psi_{\Omega_3}(\Omega_\omega\cdot\Omega)))\\ (0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(2,1,0)\\(2,2,1)&=&\psi_\Omega(\Omega_\omega\cdot\Omega+\psi_{\Omega_2}(\Omega_\omega\cdot\Omega+\Omega_\omega))\\ (0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)\\(4,2,0)&=&\psi_\Omega(\Omega_\omega\cdot\Omega+\psi_{\Omega_2}(\Omega_\omega\cdot\psi_{\Omega_2}(0)))\\ (0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)\\ (4,2,0)(2,2,0)(3,3,1)(4,1,0)(5,2,0) &=&\psi_\Omega(\Omega_\omega\cdot\Omega+\psi_{\Omega_2}(\Omega_\omega\cdot\psi_{\Omega_2}(0)+\psi_{\Omega_3}(\Omega_\omega\cdot\psi_{\Omega_2}(0))))\\ (0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,1,0)\\ (4,2,0)(2,2,1)&=&\psi_\Omega(\Omega_\omega\cdot\Omega+\psi_{\Omega_2}(\Omega_\omega\cdot\psi_{\Omega_2}(0)+\Omega_\omega))\\ (0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,2,0)&=&\psi_\Omega(\Omega_\omega\cdot\Omega+\psi_{\Omega_2}(\Omega_\omega\cdot\Omega_2))\\ (0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,2,0)\\ (2,2,0)(3,3,1)(4,2,0)&=&\psi_\Omega(\Omega_\omega\cdot\Omega+\psi_{\Omega_2}(\Omega_\omega\cdot\Omega_2+\psi_{\Omega_3}(\Omega_\omega\cdot\Omega_2)))\\ (0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,2,0)\\ (2,2,1)&=&\psi_\Omega(\Omega_\omega\cdot\Omega+\psi_{\Omega_2}(\Omega_\omega\cdot\Omega_2+\psi_{\Omega_3}(\Omega_\omega\cdot\Omega_2+\Omega _\omega)))\\ (0,0,0)(1,1,1)(2,1,0)(1,1,0)(2,2,1)(3,2,0)\\ (2,2,0)(3,3,1)(4,3,0)&=&\psi_\Omega(\Omega_\omega\cdot\Omega+\psi_{\Omega_2}(\Omega_\omega\cdot\Omega_2+\psi_{\Omega_3}(\Omega_\omega\cdot\Omega_3)))\\ (0,0,0)(1,1,1)(2,1,0)(1,1,1)&=&\psi_\Omega(\Omega_\omega\cdot\Omega +\Omega_\omega)\\ (0,0,0)(1,1,1)(2,1,0)(3,2,0)&=&\psi_\Omega(\Omega_\omega\cdot\psi_{\Omega_2}(0))\\ (0,0,0)(1,1,1)(2,1,0)(3,2,1)&=&\psi_\Omega(\Omega_\omega\cdot\psi_{\Omega_2}(\Omega_\omega))\\ (0,0,0)(1,1,1)(2,1,0)(3,2,1)(4,1,0)&=&\psi_\Omega(\Omega_\omega\cdot\psi_{\Omega_2}(\Omega_\omega\cdot\Omega))\\ (0,0,0)(1,1,1)(2,1,0)(3,2,1)(4,1,0)(1,1,0)\\ (2,2,1)(3,2,0)(4,3,1)(5,2,0)&=&\psi_\Omega(\Omega_\omega\cdot\psi_{\Omega_2}(\Omega_\omega\cdot\Omega)+\psi_{\Omega_2}(\Omega_\omega\cdot\psi_{\Omega_3}(\Omega_\omega\cdot\Omega_2)))\\ (0,0,0)(1,1,1)(2,1,0)(3,2,1)(3,1,0)(1,1,1)&=&\psi_\Omega(\Omega_\omega\cdot\psi_{\Omega_2}(\Omega_\omega\cdot\Omega)+\Omega_\omega)\\ (0,0,0)(1,1,1)(2,1,1)&=&\psi_\Omega(\Omega_\omega^2)\\ (0,0,0)(1,1,1)(2,1,1)(3,1,1)&=&\psi_\Omega(\Omega_\omega^{\Omega_\omega})\\ (0,0,0)(1,1,1)(2,2,0)&=&\psi_\Omega(\psi_{\Omega_{\omega+1}}(0))\\ &=&\psi(\psi_{\psi_\omega(0)[1]}(0))\\ (0,0,0)(1,1,1)(2,2,0)(3,1,1)&=&\psi_\Omega(\psi_{\Omega_{\omega+1}}(\Omega_\omega))\\ (0,0,0)(1,1,1)(2,2,0)(3,2,0)&=&\psi_\Omega(\psi_{\Omega_{\omega+1}}(\Omega_{\omega+1}))\\ (0,0,0)(1,1,1)(2,2,0)(3,3,0)&=&\psi_\Omega(\psi_{\Omega_{\omega+1}}(\psi_{\Omega_{\omega+2}}(0)))\\ (0,0,0)(1,1,1)(2,2,0)(3,3,1)&=&\psi_\Omega(\psi_{\Omega_{\omega+1}}(\Omega_{\omega\cdot2}))\\ &=&\psi(\psi_{\psi_\omega(0)[1]}(\psi_{\psi_\omega(0)[\omega]}(0)))\\ (0,0,0)(1,1,1)(2,2,0)(3,3,1)(4,4,0)&=&\psi_\Omega(\psi_{\Omega_{\omega+1}}(\psi_{\Omega_{\omega\cdot2+1}}(0)))\\ &=&\psi(\psi_{\psi_\omega(0)[1]}(\psi_{\psi_{\psi_\omega(0)[\omega]}(0)[1]}(0)))\\ (0,0,0)(1,1,1)(2,2,1)&=&\psi_\Omega(\Omega_{\omega^2})\\ &=&\psi(\psi_\omega(1))\\ (0,0,0)(1,1,1)(2,2,1)(2,1,0)&=&\psi_\Omega(\Omega_{\omega^2}\cdot\Omega)\\ (0,0,0)(1,1,1)(2,2,1)(2,1,0)(1,1,1)(2,2,0)\\ (3,3,1)(4,4,1)(5,3,0)&=&\psi_\Omega(\Omega_{\omega^2}\cdot\Omega+\psi_{\Omega_{\omega+1}}(\Omega _{\omega^2}\cdot\Omega_{\omega+1}))\\ (0,0,0)(1,1,1)(2,2,1)(2,1,0)(1,1,1)(2,2,1)&=&\psi_\Omega(\Omega_{\omega^2}\cdot\Omega+\Omega_{\omega^2})\\ (0,0,0)(1,1,1)(2,2,1)(2,2,0)&=&\psi_\Omega(\psi_{\Omega_{\omega^2+1}}(0))\\ (0,0,0)(1,1,1)(2,2,1)(2,2,0)(3,3,1)&=&\psi_\Omega(\psi_{\Omega_{\omega^2+1}}(\Omega_{\omega^2+\omega}))\\ &=&\psi(\psi_{\psi_\omega(1)[1]}(\psi_{\psi_\omega(1)[\omega]}(0)))\\ (0,0,0)(1,1,1)(2,2,1)(2,2,0)(3,3,1)(4,4,1)&=&\psi_\Omega(\psi_{\Omega_{\omega^2+1}}(\Omega_{\omega^2\cdot2}))\\ &=&\psi(\psi_{\psi_\omega(1)[1]}(\psi_{\psi_\omega(1)[\omega]}(1)))\\ (0,0,0)(1,1,1)(2,2,1)(2,2,1)&=&\psi_\Omega(\Omega_{\omega^3})\\ &=&\psi(\psi_\omega(2))\\ (0,0,0)(1,1,1)(2,2,1)(3,0,0)&=&\psi_\Omega(\Omega_{\omega^\omega})\\ &=&\psi(\psi_\omega(\omega))\\ (0,0,0)(1,1,1)(2,2,1)(3,0,0)(4,4,1)&=&\psi_\Omega(\Omega_{\psi_\Omega(\Omega_\omega)})\\ (0,0,0)(1,1,1)(2,2,1)(3,1,0)&=&\psi_\Omega(\Omega_\Omega)\\ &=&\psi(\psi_\omega(\psi_2(0)))\\ .......(2,2,0)(3,3,1)(4,4,1)(4,3,0)&=&\psi_{\psi_\omega(\psi_2(0))[1]}(\psi_{\psi_\omega(\psi_2(0))[\omega]}(\psi_{\psi_\omega(\psi_2(0))[2]}(0)))\\ (0,0,0)(1,1,1)(2,2,1)(3,1,0)(2,2,1)&=&\psi_{\Omega}(\Omega_{\Omega\cdot\omega})\\ &=&\psi(\psi_\omega(\psi_2(0)+1))\\ (0,0,0)(1,1,1)(2,2,1)(3,1,0)(2,2,1)&=&\psi_{\Omega}(\Omega_{\Omega_\omega})\\ &=&\psi(\psi_\omega(\psi_\omega(0)))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)&=&\psi_\Omega(\psi_I(0))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,0)&=&\psi_\Omega(\psi_{\Omega_{\psi_I(0)+1}}(0))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,0)(3,3,1)&=&\psi_\Omega(\psi_{\Omega_{\psi_I(0)+1}}(\Omega_{\psi_I(0)+\omega}))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,0)(3,3,1)\\ (4,4,1)(5,1,1)(6,2,1)(7,2,0)&=&\psi_\Omega(\psi_{\Omega_{\psi_I(0)+1}}(\Omega_{\psi_I(0)+\psi_I(0)}))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,0)(3,3,1)\\ (4,4,1)(5,1,1)(6,2,1)(7,2,0)(4,4,1)&=&\psi_\Omega(\psi_{\Omega_{\psi_I(0)+1}}(\Omega_{\psi_I(0)\cdot\omega}))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,0)(3,3,1)\\ (4,4,1)(5,1,1)(6,2,1)(7,2,0)(6,2,0)&=&\psi_\Omega(\psi_{\Omega_{\psi_I(0)+1}}(\Omega_{\psi_{\Omega_{\psi_I(0)+1}}(0)}))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,0)(3,3,1)\\ (4,4,1)(5,2,0)&=&\psi_\Omega(\psi_{\Omega_{\psi_I(0)+1}}(\Omega_{\Omega_{\psi_I(0)+1}}))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,0)(3,3,1)\\ (4,4,1)(5,3,0)&=&\psi_\Omega(\psi_{\Omega_{\psi_I(0)+1}}(\Omega_{\psi_{\Omega_{\psi_I(0)+2}}(\Omega_{\Omega_{\psi_I(0)+2}})}))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,0)(3,3,1)\\ (4,4,1)(5,3,1)&=&\psi_\Omega(\psi_{\Omega_{\psi_I(0)+1}}(\Omega_{\Omega_{\psi_I(0)+\omega}}))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,0)(3,3,1)\\ (4,4,1)(5,3,1)(6,4,1)(7,2,0)&=&\psi_\Omega(\psi_{\Omega_{\psi_I(0)+1}}(\Omega_{\Omega_{\Omega_{\psi_I(0)+1}}}))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,0)(3,3,1)\\ (4,4,1)(5,4,0)&=&\psi_\Omega(\psi_{\Omega_{\psi_I(0)+1}}(\psi_I(1)))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,0)(3,3,1)\\ (4,4,1)(5,4,0)(4,4,0)&=&\psi_\Omega(\psi_{\Omega_{\psi_I(0)+1}}(\psi_{\Omega_{\psi_I(1)+1}}(0)))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,0)(3,3,1)\\ (4,4,1)(5,4,0)(4,4,0)(5,5,1)(6,6,1)(7,6,0)&=&\psi_\Omega(\psi_{\Omega_{\psi_I(0)+1}}(\psi_{\Omega_{\psi_I(1)+1}}(\psi_I(2))))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,1)&=&\psi_\Omega(\psi_I(\omega))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,1)(1,1,0)\\ (2,2,1)(3,3,1)(4,3,0)(3,3,1)&=&\psi_\Omega(\psi_I(\omega)+\psi_{\Omega_2}(\psi_I(\omega)))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,1)(1,1,1)\\ (2,2,1)(3,2,0)(2,2,1)&=&\psi_\Omega(\psi_I(\omega)+\psi_{\Omega_{\psi_I(0)}}(\psi_I(\omega)))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,1)(2,2,0)\\ (3,3,1)(4,4,0)&=&\psi_\Omega(\psi_{\Omega_{\psi_I(\omega)}}(\psi_I(\omega+1)))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,1)(2,2,0)\\ (3,3,1)(4,4,0)(3,3,1)&=&\psi_\Omega(\psi_{\Omega_{\psi_I(\omega)}}(\psi_I(\omega\cdot2)))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,1)(2,2,1)&=&\psi_\Omega(\psi_I(\omega^2))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,1)(3,0,0)&=&\psi_\Omega(\psi_I(\omega^\omega))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,1)(3,1,1)&=&\psi_\Omega(\psi_I(\Omega_\omega))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,1)(3,1,1)\\ (4,2,1)(5,2,0)&=&\psi_\Omega(\psi_I(\psi_I(0)))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,1)(3,1,1)\\ (4,2,1)(5,2,0)(4,2,1)(5,1,1)(6,2,1)(7,2,0)&=&\psi_\Omega(\psi_I(\psi_I(\psi_I(0))))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(2,2,1)(3,2,0)&=&\psi_\Omega(\psi_I(I))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(3,0,0)&=&\psi_\Omega(\psi_I(I\cdot\omega))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(3,2,0)&=&\psi_\Omega(\psi_I(I^2))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(4,0,0)&=&\psi_\Omega(\psi_I(I^\omega))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(4,2,0)&=&\psi_\Omega(\psi_I(I^I))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(4,3,0)&=&\psi_\Omega(\psi_I(\psi_{\Omega_{I+1}}(0)))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(4,3,1)&=&\psi_\Omega(\psi_I(\psi_{\Omega_{I+1}}(\Omega_{I+\omega}))))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(4,3,1)(6,4,1)\\ (7,2,0)&=&\psi_\Omega(\psi_I(\psi_{\Omega_{I+1}}(\Omega_{I\cdot2})))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(4,3,1)(6,4,1)\\ (7,2,0)(6,4,1)&=&\psi_\Omega(\psi_I(\psi_{\Omega_{I+1}}(\Omega_{I\cdot\omega})))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(4,3,1)(6,4,1)\\ (7,3,0)&=&\psi_\Omega(\psi_I(\psi_{\Omega_{I+1}}(\Omega_{\Omega_{I+1}})))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(4,3,1)(6,4,1)\\ (7,3,1)&=&\psi_\Omega(\psi_I(\psi_{\Omega_{I+1}}(\Omega_{\Omega_{I+\omega}})))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(4,3,1)(6,4,1)\\ (7,3,1)(8,4,1)(9,3,0)&=&\psi_\Omega(\psi_I(\psi_{\Omega_{I+1}}(\Omega_{\Omega_{\Omega_{I+1}}})))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(4,3,1)(6,4,1)\\ (7,4,0)&=&\psi_\Omega(\psi_I(\psi_{\Omega_{I+1}}(\psi_{I_2}(0))))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(4,3,1)(6,4,1)\\ (7,4,0)(5,4,0)&=&\psi_\Omega(\psi_I(\psi_{\Omega_{I+1}}(\psi_{\psi_{I_2}(0)+1}(0))))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(4,3,1)(6,4,1)\\ (7,4,0)(5,4,1)(7,4,0)&=&\psi_\Omega(\psi_I(\psi_{\Omega_{I+1}}(\psi_{I_2}(I_2))))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,0)(4,3,1)(6,4,1)\\ (7,4,0)(8,5,1)(9,6,1)(10,6,0)&=&\psi_\Omega(\psi_I(\psi_{\Omega_{I+1}}(\psi_{I_2}(\psi_{\Omega_{I_2+1}}(\psi_{I_3}(0))))))\\ (0,0,0)(1,1,1)(2,2,1)(3,2,1)&=&\psi_\Omega(\psi_{I_\omega}(0))\\ &=&\psi_\Omega(\psi_I(I_{\omega}))\\ \end{array}


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