A148294 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, 1, 1), (0, 0, 1), (1, 0, -1)}.

1, 1, 2, 5, 13, 35, 110, 332, 1074, 3607, 12120, 41835, 148879, 525959, 1904427, 6995590, 25659595, 95591032, 360036559, 1353702230, 5153002842, 19759502031, 75714017272, 292822792645, 1138947841638, 4427470127513, 17339998869034, 68210151850507, 268226913204807, 1061159916625160, 4213133936804945

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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

Crossrefs

Sequence in context: A148291 A148292 A148293 * A148295 A288540 A327014

Adjacent sequences: A148291 A148292 A148293 * A148295 A148296 A148297

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved