A148292 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, 1), (-1, 1, 0), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 5, 13, 35, 109, 330, 1066, 3545, 12002, 41340, 146669, 520408, 1892267, 6920385, 25633619, 95666879, 361061450, 1367616912, 5237966081, 20117499658, 77914834275, 302809077698, 1184609064244, 4647630453801, 18345208193807, 72570711986662, 288615807565744, 1150213287552401, 4604529233197752

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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[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, 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: A151259 A149853 A148291 * A148293 A148294 A148295

Adjacent sequences: A148289 A148290 A148291 * A148293 A148294 A148295

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved