A149308 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, 0, 1), (-1, 1, 0), (1, -1, 1), (1, 1, 0)}.

1, 1, 4, 11, 48, 160, 722, 2639, 12302, 47370, 223638, 891897, 4264396, 17419445, 83826126, 348887426, 1688966347, 7129241116, 34645839644, 147958621019, 721420188206, 3109847454343, 15201470731470, 66054784486884, 323562953643088, 1415428375412890, 6945538586626436, 30561041741638814

Offset

0,3

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, -1 + j, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 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: A149305 A149306 A149307 * A149309 A372115 A149310

Adjacent sequences: A149305 A149306 A149307 * A149309 A149310 A149311

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved