A151176 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), (-1, 1, -1), (1, 0, 0), (1, 0, 1), (1, 1, 1)}.

1, 3, 12, 49, 224, 1003, 4768, 22205, 107427, 510781, 2496415, 12023925, 59130180, 287233639, 1418316408, 6930885083, 34321022015, 168447987219, 835840981998, 4115763918768, 20453419308754, 100969353598418, 502346798505766, 2484796068193661, 12373436347093319, 61301180276682612, 305471913772603733

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, j, -1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + 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: A301456 A151174 A151175 * A151177 A344419 A002179

Adjacent sequences: A151173 A151174 A151175 * A151177 A151178 A151179

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved