A148181 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, -1), (-1, -1, 1), (-1, 1, 0), (1, -1, 1), (1, 0, 0)}.

1, 1, 2, 4, 12, 28, 92, 251, 888, 2597, 9537, 29203, 109909, 349642, 1347960, 4412258, 17254200, 57702511, 228126260, 776452797, 3103037189, 10722616957, 43192929605, 151123294126, 612533426234, 2165705471538, 8830353514411, 31514065364332, 129137543384627, 464637658064443, 1911685246445333

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, 1 + j, -1 + k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, 1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + j, 1 + 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: A148178 A148179 A148180 * A331687 A148182 A148183

Adjacent sequences: A148178 A148179 A148180 * A148182 A148183 A148184

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved