A150803 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, 0, 0), (1, -1, 0), (1, 0, 1), (1, 1, -1), (1, 1, 0)}.

1, 2, 8, 31, 133, 574, 2581, 11673, 53840, 249646, 1170407, 5511127, 26129428, 124321268, 594254165, 2848588175, 13700158744, 66041949214, 319147827858, 1545187859952, 7495627416751, 36417552289909, 177207833389215, 863415899380530, 4212158066864544, 20571509197944074, 100573540139228301

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[-1 + i, 1 + j, k, -1 + n] + aux[1 + i, 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: A150800 A150801 A150802 * A150804 A150805 A150806

Adjacent sequences: A150800 A150801 A150802 * A150804 A150805 A150806

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved