A148994 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, 1), (1, -1, 0), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 9, 33, 116, 458, 1760, 7255, 29393, 124655, 521829, 2256316, 9664098, 42389957, 184646747, 818911689, 3612785095, 16162919544, 72022055993, 324502937396, 1457666871909, 6606325339738, 29871625322652, 136051924400319, 618569873615481, 2829217786121719, 12923163826023643, 59323860283383890

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[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, 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: A148991 A148992 A148993 * A148995 A148996 A255713

Adjacent sequences: A148991 A148992 A148993 * A148995 A148996 A148997

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved