A148302 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), (0, 1, -1), (1, 0, -1), (1, 0, 0)}.

1, 1, 2, 5, 13, 38, 113, 365, 1191, 4067, 14144, 50226, 182525, 669319, 2506400, 9447969, 36149151, 139432800, 542694872, 2132023358, 8422627133, 33567994566, 134391139541, 541815720672, 2194797616118, 8935440795783, 36560925539999, 150149210854266, 619576859264739, 2564765323038883

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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[-1 + i, j, 1 + k, -1 + n] + aux[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: A149856 A320175 A064384 * A149857 A001475 A360271

Adjacent sequences: A148299 A148300 A148301 * A148303 A148304 A148305

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved