A149344 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, 0), (1, 0, -1), (1, 0, 1), (1, 1, -1)}.

1, 1, 4, 12, 42, 144, 558, 2115, 8365, 32835, 134882, 549528, 2286600, 9483263, 40231902, 170084068, 727936899, 3111265619, 13473412479, 58262030565, 253926141635, 1106269232727, 4859865964520, 21339504293971, 94204444105176, 415914724112337, 1846601894388353, 8198945952462282

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, 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: A308371 A052303 A017942 * A178078 A135489 A100217

Adjacent sequences: A149341 A149342 A149343 * A149345 A149346 A149347

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved