A148640 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, 1, 0), (-1, 1, 1), (0, 1, -1), (1, 0, 0)}.

1, 1, 3, 6, 22, 62, 215, 708, 2509, 8925, 32078, 118661, 440178, 1657992, 6278939, 24033464, 92682133, 358921659, 1400617687, 5489703720, 21631282920, 85549496243, 339806449140, 1354961614440, 5419329749825, 21747200755159, 87523233075117, 353243743565773, 1429174212609720, 5796355553493317

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A148637 A148638 A148639 * A148641 A148642 A049415

Adjacent sequences: A148637 A148638 A148639 * A148641 A148642 A148643

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved