A149055 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, -1)}.

1, 1, 3, 10, 40, 155, 661, 2809, 12388, 55098, 249064, 1135248, 5225124, 24208799, 112873953, 528935624, 2489987847, 11767157943, 55803419262, 265442664895, 1266114276385, 6053949599553, 29011329072416, 139305020533736, 670130501757298, 3229062672948896, 15583269734938239, 75310011395231900

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, 1 + 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: A009692 A149053 A149054 * A254535 A093639 A089005

Adjacent sequences: A149052 A149053 A149054 * A149056 A149057 A149058

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved