A149059 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), (0, 1, 1), (1, -1, 1), (1, 1, -1)}

1, 1, 3, 10, 42, 162, 730, 3082, 14290, 63336, 298514, 1361600, 6486758, 30142468, 144686738, 681021198, 3287160352, 15617444040, 75703276070, 362216229252, 1761679987258, 8475504487054, 41333249569972, 199728941712302, 976209612966736, 4734057461781154, 23181770959944304, 112750725767858324

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, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[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: A308951 A295236 A214835 * A129878 A094558 A074511

Adjacent sequences: A149056 A149057 A149058 * A149060 A149061 A149062

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved