A148504 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, -1, 1), (-1, 0, 0), (-1, 1, 0), (1, 0, 0)}.

1, 1, 3, 5, 17, 34, 121, 265, 997, 2330, 9161, 22428, 91109, 230853, 956887, 2486209, 10456869, 27707670, 118000345, 317767912, 1368722965, 3736854701, 16249643675, 44881448060, 196661563637, 548519721819, 2418707405661, 6803051692760, 30166125522587, 85475572870974, 380941790864009, 1086489020586897

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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[1 + i, -1 + j, k, -1 + n] + aux[1 + i, j, k, -1 + n] + aux[1 + i, 1 + 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: A056816 A156761 A151261 * A148505 A148506 A148507

Adjacent sequences: A148501 A148502 A148503 * A148505 A148506 A148507

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved