A149288 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, 0, 1), (0, 1, -1), (1, -1, 1), (1, 1, 0)}

1, 1, 4, 11, 44, 167, 688, 2890, 12419, 54454, 241769, 1087412, 4935565, 22595510, 104165606, 483135030, 2252977513, 10554133201, 49650073966, 234409724447, 1110396592564, 5275286144880, 25129241775010, 119993639461761, 574241452799050, 2753632778141387, 13228721517683888, 63660517124775179

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[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, 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: A149285 A149286 A149287 * A149289 A149290 A074410

Adjacent sequences: A149285 A149286 A149287 * A149289 A149290 A149291

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved