A148763 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, 1), (-1, 1, 1), (1, 0, 0), (1, 1, -1)}.

1, 1, 3, 7, 29, 84, 374, 1225, 5664, 19968, 94395, 349513, 1674794, 6425660, 31078444, 122470535, 596237427, 2399354545, 11737547791, 48037100858, 235856644518, 978750425364, 4819191119645, 20232322464195, 99844120636619, 423336713068232, 2092891044655529, 8949655914325527, 44310533191971144

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A186732 A148762 A096064 * A148764 A148765 A148766

Adjacent sequences: A148760 A148761 A148762 * A148764 A148765 A148766

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved