A151062 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), (0, 0, 1), (0, 1, 0), (1, 0, 0), (1, 1, -1)}.

1, 3, 10, 38, 155, 655, 2849, 12669, 57209, 261589, 1208492, 5628460, 26393977, 124495365, 590093208, 2808834386, 13419588807, 64319800651, 309159921846, 1489772727522, 7194990913263, 34818968871025, 168807738275493, 819749583094019, 3986745249725499, 19415473533566595, 94671145392024186

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[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: A109085 A259690 A001002 * A000902 A151063 A103138

Adjacent sequences: A151059 A151060 A151061 * A151063 A151064 A151065

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved