A150543 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, 0, 0), (0, 1, 1), (1, 0, -1), (1, 1, 0)}.

1, 2, 7, 26, 103, 432, 1858, 8189, 36689, 166642, 765147, 3543811, 16535520, 77630619, 366395694, 1737136637, 8268646493, 39494682800, 189220899321, 909028224403, 4377606117144, 21127109933769, 102163191694267, 494902293671261, 2401292042004619, 11668357622150545, 56775333500447576, 276596733938294932

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, 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: A150540 A150541 A150542 * A150544 A345884 A150545

Adjacent sequences: A150540 A150541 A150542 * A150544 A150545 A150546

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved