A149680 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), (1, -1, 0), (1, 0, -1), (1, 1, 1)}.

1, 1, 5, 17, 67, 257, 1123, 4609, 20149, 86133, 384359, 1678189, 7555497, 33547783, 152248901, 683700859, 3122031341, 14143050233, 64896996275, 296006914703, 1363855881123, 6254614166669, 28916599470335, 133206245008099, 617653700379543, 2855834510009821, 13275537310532085, 61575158420969649

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[-1 + i, 1 + j, 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: A059847 A149678 A149679 * A149681 A149682 A149683

Adjacent sequences: A149677 A149678 A149679 * A149681 A149682 A149683

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved