A151094 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), (0, 0, 1), (0, 1, 0), (0, 1, 1), (1, 1, -1)}.

1, 3, 11, 43, 177, 755, 3303, 14727, 66641, 305107, 1410179, 6568867, 30799777, 145214819, 687917407, 3272245311, 15621109601, 74807650147, 359245134843, 1729472608539, 8344519837009, 40341962006675, 195387635818967, 947870317985783, 4605206781143857, 22404849653643955, 109138628861675123

Offset

0,2

Links

Table of n, a(n) for n=0..26.

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[i, -1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[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: A151091 A151092 A151093 * A339043 A103821 A151095

Adjacent sequences: A151091 A151092 A151093 * A151095 A151096 A151097

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved