A150710 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), (0, 0, 1), (0, 1, -1), (1, 0, 1), (1, 1, -1)}.

1, 2, 8, 27, 116, 475, 2093, 9225, 41812, 190557, 881483, 4100209, 19231374, 90670058, 429730691, 2044916451, 9768824521, 46811676808, 224969448854, 1083897615629, 5233923365141, 25324373396373, 122757487998436, 596026077271773, 2898222779227043, 14112145883113578, 68800737149631772

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[i, -1 + j, 1 + k, -1 + n] + aux[i, j, -1 + 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: A054109 A305256 A323613 * A150711 A150712 A150713

Adjacent sequences: A150707 A150708 A150709 * A150711 A150712 A150713

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved