A148143 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, 0, 0), (0, -1, 1), (0, 1, 0), (1, 1, -1)}.

1, 1, 2, 4, 11, 29, 86, 259, 813, 2624, 8625, 28963, 98574, 340054, 1186705, 4179149, 14852005, 53163212, 191594122, 694672103, 2531984454, 9274549301, 34120379194, 126031251666, 467241100691, 1738008143484, 6485031450788, 24266496392659, 91043130878318, 342414368714079, 1290751411994408, 4875908066603452

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, -1 + j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A148141 A317879 A148142 * A148144 A148145 A052869

Adjacent sequences: A148140 A148141 A148142 * A148144 A148145 A148146

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved