A148991 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, 1, -1), (0, 1, 1), (1, -1, 1), (1, 0, -1)}.

1, 1, 3, 9, 33, 115, 459, 1811, 7463, 31109, 132832, 571567, 2500163, 11007204, 48984490, 219405461, 989521381, 4489102130, 20470167188, 93784099031, 431525119196, 1992979449935, 9237841668792, 42953637051069, 200319106810759, 936760666262082, 4391543909233451, 20636163505678186

Offset

0,3

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, j, 1 + k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A047117 A148990 A184512 * A148992 A148993 A148994

Adjacent sequences: A148988 A148989 A148990 * A148992 A148993 A148994

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved