A148027 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, -1), (-1, -1, 1), (-1, 1, 0), (1, 0, 0), (1, 1, -1)}.

1, 1, 2, 3, 8, 17, 50, 123, 424, 1157, 4118, 11905, 44192, 134684, 512943, 1629383, 6357396, 20847452, 83017169, 279238026, 1129642409, 3880637177, 15899231818, 55624783220, 230299526462, 818618381183, 3420635838769, 12326916547038, 51935674211138, 189400178549430, 803816332741202, 2962211262398908

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[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 1 + 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: A148025 A324615 A148026 * A148028 A148029 A148030

Adjacent sequences: A148024 A148025 A148026 * A148028 A148029 A148030

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved