A150962 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, 0, 1), (1, 0, -1), (1, 1, 0), (1, 1, 1)}.

1, 2, 9, 35, 166, 727, 3538, 16294, 80160, 378927, 1874930, 9000443, 44683110, 216630208, 1077697787, 5260220811, 26204060817, 128518455419, 640809487729, 3154046495137, 15736623881298, 77664193244089, 387673662776003, 1917272347984752, 9573667095262513, 47425770367580942, 236876010551566137

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[-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, 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: A150959 A150960 A150961 * A150963 A150964 A150965

Adjacent sequences: A150959 A150960 A150961 * A150963 A150964 A150965

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved