A151113 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, 1, -1), (0, 1, 0), (1, 0, 1), (1, 1, 0)}.

1, 3, 11, 45, 191, 839, 3763, 17143, 79001, 367467, 1721501, 8113463, 38427526, 182765903, 872362732, 4176782763, 20051987169, 96495251804, 465340310874, 2248302465257, 10881166038747, 52742694960132, 256008579523104, 1244226141564253, 6054114216345159, 29489533545009286, 143785608373214375

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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, j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + 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: A151112 A083324 A238578 * A151114 A083878 A363183

Adjacent sequences: A151110 A151111 A151112 * A151114 A151115 A151116

Keyword

nonn,walk,changed

Author

Manuel Kauers, Nov 18 2008

Status

approved