A150219 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), (0, 1, 1), (1, 0, 0), (1, 1, -1)}.

1, 2, 6, 21, 82, 321, 1315, 5459, 23101, 99239, 430761, 1885010, 8314081, 36891946, 164646168, 738475180, 3325764202, 15034489911, 68193338795, 310244886356, 1415392174360, 6473319142842, 29672579428926, 136297729801830, 627265676209046, 2891910000783213, 13354629064337700, 61764320784189527

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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, j, k, -1 + n] + aux[i, -1 + 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: A150216 A150217 A150218 * A150220 A168653 A279567

Adjacent sequences: A150216 A150217 A150218 * A150220 A150221 A150222

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved