A150720 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), (-1, 0, -1), (0, 0, 1), (1, 0, -1), (1, 1, 1)}.

1, 2, 8, 28, 118, 488, 2136, 9380, 42070, 190154, 870416, 4008548, 18600334, 86701702, 406264347, 1911554475, 9028250128, 42775979989, 203243898732, 968197218325, 4623364495768, 22124820603902, 106081304417305, 509507668612067, 2451161901643558, 11810158787699635, 56983234571722242, 275292377784395038

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, j, -1 + k, -1 + n] + aux[1 + 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: A217720 A151300 A150719 * A150721 A150722 A150723

Adjacent sequences: A150717 A150718 A150719 * A150721 A150722 A150723

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved