A148524 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, -1, 0), (-1, -1, 1), (-1, 0, -1), (1, 1, 0)}.

1, 1, 3, 5, 19, 39, 155, 349, 1451, 3479, 14779, 36915, 159715, 411423, 1802107, 4751245, 21023355, 56465431, 251821403, 686573131, 3082102019, 8508596927, 38404325915, 107140788035, 485841061747, 1367653750399, 6226563544395, 17664926197199, 80704113286291, 230524444392639, 1056402790056571, 3035710539009645

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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, k, -1 + n] + aux[1 + i, j, 1 + k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A128066 A273020 A148523 * A148525 A148526 A148527

Adjacent sequences: A148521 A148522 A148523 * A148525 A148526 A148527

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved