A149080 Number of walks within N^3 (the first octant of Z^3) starting at (0,0,0) and consisting of n steps taken from {(-1, -1, 1), (-1, 1, -1), (1, -1, -1), (1, 1, 1)}.

1, 1, 4, 7, 28, 70, 280, 787, 3148, 9526, 38104, 120922, 483688, 1586248, 6344992, 21342211, 85368844, 292614958, 1170459832, 4075263994, 16301055976, 57458624464, 229834497856, 818786992666, 3275147970664, 11769370428016, 47077481712064, 170479948663240, 681919794652960, 2485397985195496

Offset

0,3

Links

Table of n, a(n) for n=0..29.

A. Bostan and M. Kauers, 2008. Automatic Classification of Restricted Lattice Walks, ArXiv 0811.2899.

Mathematica

aux[i_Integer, j_Integer, k_Integer, n_Integer] := Which[Min[i, j, k, n] < 0 || Max[i, j, k] > n, 0, n == 0, KroneckerDelta[i, j, k, n], True, aux[i, j, k, n] = aux[-1 + i, -1 + j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A149077 A149078 A149079 * A366314 A176966 A117977

Adjacent sequences: A149077 A149078 A149079 * A149081 A149082 A149083

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved