A149060 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, 0, 0), (-1, 0, 1), (0, 1, 1), (1, -1, 0), (1, 0, -1)}.

1, 1, 3, 11, 38, 147, 587, 2406, 10215, 43810, 191420, 846279, 3777172, 17035113, 77322677, 353531629, 1625496758, 7511140978, 34874728630, 162546596481, 760497205550, 3569629858872, 16805317213158, 79336544291945, 375460389917649, 1781012503780536, 8466003357569875, 40321831074573891

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + k, -1 + n] + aux[1 + i, 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: A026943 A307571 A047096 * A151468 A289989 A295263

Adjacent sequences: A149057 A149058 A149059 * A149061 A149062 A149063

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved