A149426 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, 0), (0, 1, -1), (1, 0, 1), (1, 1, -1)}

1, 1, 4, 13, 43, 165, 653, 2554, 10353, 43406, 181669, 766756, 3300981, 14302542, 62073273, 272025803, 1201510207, 5316833661, 23625660731, 105633697288, 473708034708, 2128697603138, 9603529706857, 43467271246910, 197075677833424, 895605279361840, 4081386577467745, 18632961639799468

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, j, -1 + k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, j, 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: A297928 A363366 A113986 * A042767 A286175 A252831

Adjacent sequences: A149423 A149424 A149425 * A149427 A149428 A149429

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved