A148927 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, 0), (0, 1, -1), (1, -1, 0), (1, 0, 1)}.

1, 1, 3, 9, 27, 95, 336, 1244, 4781, 18477, 73322, 296046, 1207052, 4987746, 20793422, 87421781, 370790380, 1582749908, 6797872346, 29363763117, 127460556855, 555943978956, 2435259031468, 10708170406171, 47256735443271, 209242372905137, 929354290664595, 4139817383383738, 18490171873669054

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, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A148925 A148926 A146573 * A148928 A029527 A325047

Adjacent sequences: A148924 A148925 A148926 * A148928 A148929 A148930

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved