A148283 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), (-1, 0, 1), (0, 1, 0), (1, -1, 0)}.

1, 1, 2, 5, 12, 32, 92, 277, 823, 2608, 8602, 27487, 91954, 317118, 1070466, 3694465, 13109697, 46047042, 162460455, 588094407, 2123508899, 7635228131, 28024695724, 103185183237, 377404197974, 1399263641624, 5225389114090, 19399013263762, 72524456841915, 273643912462107, 1028680862533408, 3875666661175306

Offset

0,3

Links

Table of n, a(n) for n=0..31.

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[i, -1 + j, 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]]; Table[Sum[aux[i, j, k, n], {i, 0, n}, {j, 0, n}, {k, 0, n}], {n, 0, 10}]

Crossrefs

Sequence in context: A363240 A148281 A148282 * A218781 A363682 A002838

Adjacent sequences: A148280 A148281 A148282 * A148284 A148285 A148286

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved