A150000 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), (0, 0, -1), (0, 1, 0), (1, 0, 1)}.

1, 2, 5, 17, 60, 211, 788, 3087, 12031, 47612, 193723, 793555, 3259183, 13568871, 57057573, 240409463, 1018554059, 4350518045, 18652248413, 80161322115, 346233726610, 1501989852179, 6529325778008, 28460597180882, 124509570144503, 546038156698710, 2398821135999848, 10564714909607449

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, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 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: A148414 A306586 A232217 * A150001 A150002 A150003

Adjacent sequences: A149997 A149998 A149999 * A150001 A150002 A150003

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved