A148999 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, 0, 1), (1, 0, -1), (1, 1, -1), (1, 1, 0)}.

1, 1, 3, 9, 34, 114, 484, 1809, 7983, 32097, 144898, 609838, 2801604, 12159600, 56608738, 251279146, 1181576856, 5336084300, 25285120286, 115751190584, 551839279807, 2553932777703, 12236239440844, 57135960511101, 274872856802229, 1292984639225590, 6241894883118289, 29543497529355390

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, -1 + j, k, -1 + n] + aux[-1 + i, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A100076 A213907 A377145 * A149000 A160963 A149001

Adjacent sequences: A148996 A148997 A148998 * A149000 A149001 A149002

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved