A148580 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), (-1, 1, 0), (0, 0, -1), (1, 0, 0)}.

1, 1, 3, 6, 20, 52, 175, 538, 1835, 6128, 21452, 75459, 270156, 979587, 3595733, 13307639, 49732088, 187334205, 710915164, 2712899215, 10423811202, 40260795863, 156235895528, 609176113446, 2385812163203, 9379463583579, 37005572677217, 146538482373287, 582124546607455, 2319149328482453

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, j, k, -1 + n] + aux[i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A182299 A148579 A151263 * A148581 A148582 A148583

Adjacent sequences: A148577 A148578 A148579 * A148581 A148582 A148583

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved