A150536 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), (0, 1, -1), (0, 1, 1), (1, 0, 1)}.

1, 2, 7, 26, 102, 420, 1762, 7546, 32776, 143740, 636509, 2837470, 12723564, 57356783, 259622346, 1179671953, 5378030204, 24587733520, 112709464907, 517854785497, 2384306458458, 10998978703826, 50826959867930, 235249720011487, 1090445475090001, 5061348100981751, 23522089805096353, 109444564002516165

Offset

0,2

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, j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[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: A171711 A363293 A129482 * A307413 A326564 A271844

Adjacent sequences: A150533 A150534 A150535 * A150537 A150538 A150539

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved