A148704 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), (-1, 1, 1), (0, -1, 0), (0, 0, -1), (1, 0, 0)}.

1, 1, 3, 7, 23, 73, 255, 895, 3309, 12311, 47361, 183183, 724733, 2881317, 11647367, 47278907, 194370111, 801915951, 3341949461, 13969919759, 58876304081, 248789702749, 1058454456759, 4513481955851, 19357097166219, 83185584301713, 359242498536387, 1554197478964649, 6752629753488099

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, j, k, -1 + n] + aux[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, 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: A079061 A228724 A191638 * A283109 A339284 A057184

Adjacent sequences: A148701 A148702 A148703 * A148705 A148706 A148707

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved