A150952 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, 1, -1), (1, 0, 1), (1, 1, -1), (1, 1, 1)}.

1, 2, 9, 35, 155, 690, 3171, 14620, 68671, 323788, 1538292, 7342163, 35208637, 169337703, 817064667, 3952269649, 19158906154, 93050722532, 452711595085, 2205777113475, 10761702223075, 52568689845221, 257066371994331, 1258313530733432, 6164891958547112, 30228796740536382, 148335346441221617

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, 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: A150949 A150950 A150951 * A150953 A150954 A150955

Adjacent sequences: A150949 A150950 A150951 * A150953 A150954 A150955

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved