A148513 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, 0), (1, 0, -1), (1, 0, 0)}.

1, 1, 3, 5, 17, 36, 132, 324, 1249, 3384, 13513, 39254, 160933, 492667, 2061281, 6573859, 27953711, 92135701, 396995905, 1344484187, 5857194879, 20293100945, 89231953988, 315216303132, 1397145357480, 5018909316758, 22399731055518, 81651914667098, 366629319842832, 1353795080618278, 6111309663883855

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, -1 + j, 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: A130844 A148511 A148512 * A148514 A105894 A305411

Adjacent sequences: A148510 A148511 A148512 * A148514 A148515 A148516

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved