A148996 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), (1, -1, 1), (1, 0, 1), (1, 1, -1)}.

1, 1, 3, 9, 33, 119, 454, 1779, 7152, 29311, 122013, 514390, 2192976, 9435593, 40927132, 178767188, 785677788, 3471969333, 15417894851, 68766083151, 307921250078, 1383758689713, 6238746051177, 28211698413079, 127923279261484, 581519329356110, 2649655569254817, 12099042388429222, 55358244255747829

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, -1 + j, 1 + k, -1 + 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, 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: A148993 A148994 A148995 * A255713 A148997 A082841

Adjacent sequences: A148993 A148994 A148995 * A148997 A148998 A148999

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved