A148940 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), (0, 1, 1), (1, 0, -1)}.

1, 1, 3, 9, 29, 99, 360, 1357, 5203, 20370, 81126, 327936, 1341708, 5538553, 23057491, 96745210, 408716932, 1736757396, 7418365253, 31835377665, 137216306947, 593770969859, 2578522060500, 11233959191344, 49090715171230, 215118601209475, 945106337138974, 4162197021625413, 18370926413447123

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[i, -1 + j, -1 + 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: A239118 A239119 A238803 * A169781 A162998 A275014

Adjacent sequences: A148937 A148938 A148939 * A148941 A148942 A148943

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved