A150221 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, 0, 1), (0, 1, 0), (1, -1, 1), (1, 0, 0), (1, 1, -1)}.

1, 2, 6, 21, 83, 349, 1528, 6885, 31663, 147881, 698854, 3333119, 16013223, 77383680, 375742768, 1831622869, 8957731740, 43928634211, 215923994375, 1063428003467, 5246221788939, 25918820316508, 128212232578680, 634919400291523, 3147189891410274, 15613197779383373, 77514351786069528

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, k, -1 + n] + aux[-1 + i, 1 + j, -1 + k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, 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: A032346 A329055 A148495 * A058866 A063689 A178325

Adjacent sequences: A150218 A150219 A150220 * A150222 A150223 A150224

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved