A150215 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, 1, 1), (0, 0, 1), (1, 0, 0), (1, 1, -1)}.

1, 2, 6, 21, 81, 334, 1428, 6283, 28204, 128605, 593492, 2765382, 12986012, 61373153, 291608306, 1391797307, 6668339795, 32054662762, 154527631682, 746801740045, 3617079719503, 17553133963549, 85330109635389, 415453019286677, 2025562898443804, 9888154841078525, 48325878436856862, 236425857821312468

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, j, -1 + k, -1 + n] + aux[1 + 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: A150213 A279565 A150214 * A328434 A150216 A150217

Adjacent sequences: A150212 A150213 A150214 * A150216 A150217 A150218

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved