A150753 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), (1, 0, -1), (1, 0, 1), (1, 1, 0)}

1, 2, 8, 29, 128, 535, 2457, 10901, 51128, 234218, 1112878, 5199214, 24921000, 117962731, 568978422, 2718283582, 13173006570, 63364640061, 308188534015, 1490170288324, 7268785039974, 35289620937232, 172541852837631, 840409963463861, 4117033432155720, 20106216931458494, 98658506479952245

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, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 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: A150750 A150751 A150752 * A162066 A151302 A150754

Adjacent sequences: A150750 A150751 A150752 * A150754 A150755 A150756

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved