A148541 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, 0), (-1, 1, -1), (1, -1, -1), (1, 0, 1)}.

1, 1, 3, 5, 19, 45, 167, 463, 1773, 5347, 21243, 66329, 270741, 881867, 3635689, 12286063, 51092407, 176869405, 744179477, 2618815961, 11119042747, 39809321921, 169909694141, 617996794235, 2650782424537, 9753495957039, 42072930125253, 156287913106205, 677203467931739, 2539950992389529

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, -1 + k, -1 + n] + aux[-1 + i, 1 + 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, 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: A148538 A148539 A148540 * A148542 A148543 A148544

Adjacent sequences: A148538 A148539 A148540 * A148542 A148543 A148544

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved