A150964 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), (0, 1, -1), (1, 0, 1), (1, 1, -1), (1, 1, 1)}.

1, 2, 9, 35, 167, 727, 3563, 16352, 80886, 381375, 1894788, 9081014, 45223116, 219008539, 1092180415, 5326794486, 26587589777, 130325490701, 650857372682, 3202130594494, 15997600990943, 78926157160318, 394405772034276, 1950061998855125, 9746377213403280, 48271355722406643, 241287269353074424

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[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: A150961 A150962 A150963 * A150965 A150966 A185034

Adjacent sequences: A150961 A150962 A150963 * A150965 A150966 A150967

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved