A150560 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, 0, 0), (0, -1, 1), (0, 1, 0), (1, 0, -1), (1, 0, 1)}.

1, 2, 7, 26, 106, 443, 1931, 8532, 38556, 175744, 812102, 3775043, 17708060, 83425112, 395532431, 1881427225, 8991123869, 43077291303, 207115573368, 997843270871, 4820607972067, 23327203264218, 113127811678434, 549380905060311, 2672659561398277, 13017135794651217, 63491735107888927, 309988267330122717

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, -1 + k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A150557 A150558 A150559 * A150561 A122871 A150562

Adjacent sequences: A150557 A150558 A150559 * A150561 A150562 A150563

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved