A148215 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), (-1, 0, 0), (-1, 1, -1), (0, 1, 1), (1, -1, -1)}.

1, 1, 2, 4, 13, 31, 89, 283, 869, 2669, 8870, 29810, 98119, 333199, 1177914, 4047033, 14102749, 50959995, 181208819, 644899622, 2360104239, 8605418138, 31204155230, 115179384007, 427767584786, 1575929436375, 5862275394312, 22051157334933, 82345073867692, 308660266442344, 1171134621701716, 4423528229124228

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A077325 A148213 A148214 * A148216 A148217 A148218

Adjacent sequences: A148212 A148213 A148214 * A148216 A148217 A148218

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved