A149096 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), (-1, 1, 0), (1, -1, -1), (1, 1, 0)}.

1, 1, 4, 8, 33, 85, 368, 1075, 4794, 15211, 68980, 231773, 1063877, 3723774, 17259336, 62309667, 290989867, 1076811320, 5058555808, 19101348364, 90168012117, 346225925596, 1641065271522, 6390839122105, 30397384197953, 119817767728918, 571601039341048, 2276881667206275, 10890176289287515

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, k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A173326 A173652 A149095 * A149097 A149098 A149099

Adjacent sequences: A149093 A149094 A149095 * A149097 A149098 A149099

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved