A148358 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, 0, 0), (0, -1, 1), (0, 1, 0), (1, 0, -1), (1, 1, -1)}.

1, 1, 2, 5, 15, 45, 151, 523, 1881, 6965, 26487, 102601, 404609, 1619963, 6568854, 26939533, 111602913, 466477951, 1965296691, 8339774230, 35620899135, 153043448404, 661093944092, 2869845158073, 12514815965529, 54803343547278, 240919643876389, 1062914499955194, 4705170248152238

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A149911 A148357 A149912 * A149913 A065848 A148359

Adjacent sequences: A148355 A148356 A148357 * A148359 A148360 A148361

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved