A149908 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, -1), (0, 0, 1), (1, 0, 0)}.

1, 2, 5, 15, 45, 148, 502, 1747, 6317, 23052, 86168, 326073, 1247768, 4839365, 18891695, 74501818, 295679894, 1181086264, 4748015184, 19173354653, 77844912265, 317299791462, 1298651204383, 5334866709154, 21985427198380, 90903355567615, 376877960323436, 1566838350507980, 6530022541791072

Offset

0,2

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[1 + i, -1 + j, 1 + 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: A148355 A148356 A206302 * A149909 A149910 A149911

Adjacent sequences: A149905 A149906 A149907 * A149909 A149910 A149911

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved