A151227 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, 0), (0, 1, -1), (0, 1, 1), (1, 0, 1), (1, 1, 1)}.

1, 3, 13, 58, 272, 1292, 6233, 30279, 148033, 726688, 3578955, 17670025, 87409934, 433072383, 2148368625, 10668512572, 53024146940, 263727212519, 1312502556127, 6535377477859, 32556202388500, 162242071294643, 808793953128968, 4033095019491650, 20116380749745208, 100359576531984893

Offset

0,2

Links

Table of n, a(n) for n=0..25.

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, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 1 + j, 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: A270786 A151226 A151320 * A151228 A366676 A339881

Adjacent sequences: A151224 A151225 A151226 * A151228 A151229 A151230

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved