A150596 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, -1, 1), (0, 1, -1), (1, 0, 0), (1, 1, 1)}.

1, 2, 7, 27, 107, 470, 2033, 9086, 41227, 188036, 872685, 4059101, 19039409, 89808886, 424989379, 2022124509, 9644549971, 46156345590, 221518673285, 1065265253809, 5135590502267, 24800865960620, 119981448823525, 581410944356560, 2821159938426259, 13708276145589738, 66688481480233137

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, 1 + k, -1 + n] + aux[1 + i, 1 + 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: A192417 A150594 A150595 * A026726 A150597 A150598

Adjacent sequences: A150593 A150594 A150595 * A150597 A150598 A150599

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved