A149976 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, 1), (0, 1, -1), (0, 1, 0), (1, 0, 0)}.

1, 2, 5, 16, 56, 205, 789, 3140, 12737, 52645, 221237, 940280, 4036120, 17488141, 76333906, 335288294, 1481469377, 6579191771, 29346723435, 131438569091, 590855902974, 2664734932608, 12054081070363, 54678447163174, 248649340102252, 1133356326510669, 5177055759890923, 23695333294518261

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, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + 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: A149973 A149974 A149975 * A141201 A149977 A147771

Adjacent sequences: A149973 A149974 A149975 * A149977 A149978 A149979

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved