A149156 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, 0), (1, 0, -1), (1, 1, 0)}.

1, 1, 4, 9, 39, 112, 512, 1660, 7796, 27224, 129917, 477245, 2301281, 8769055, 42591564, 166860618, 814734888, 3262097542, 15991318693, 65159871299, 320406115972, 1324542450930, 6528900687902, 27318534528929, 134920901848093, 570376728242050, 2821473268289106, 12033776552315483, 59605851930799209

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A101529 A149154 A149155 * A149157 A149158 A142239

Adjacent sequences: A149153 A149154 A149155 * A149157 A149158 A149159

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved