A150496 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, 0, -1), (0, -1, 1), (1, 0, 0), (1, 1, 1)}.

1, 2, 7, 25, 101, 408, 1705, 7240, 31295, 136736, 601885, 2670989, 11928673, 53590728, 241750945, 1095001345, 4977673451, 22703347940, 103836508801, 476080076739, 2187828444233, 10075777711660, 46491850061587, 214890070028128, 994831853703233, 4612501654136600, 21415468660890999, 99556177340653557

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[1 + i, 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: A150493 A150494 A150495 * A150497 A150498 A150499

Adjacent sequences: A150493 A150494 A150495 * A150497 A150498 A150499

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved