A149411 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, 0, 1), (1, -1, 1), (1, 1, -1), (1, 1, 0)}.

1, 1, 4, 12, 52, 199, 895, 3792, 17523, 77968, 366808, 1679585, 7995678, 37298169, 179019270, 845838011, 4083954115, 19474918120, 94451708752, 453524961665, 2207187903123, 10654577147427, 51996035136325, 252048114887290, 1232790097312202, 5996008969942303, 29381370786364795, 143297633781459588

Offset

0,3

Links

Table of n, a(n) for n=0..27.

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, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A125529 A149409 A149410 * A149412 A259274 A109499

Adjacent sequences: A149408 A149409 A149410 * A149412 A149413 A149414

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved