A148706 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, 1), (-1, 1, 1), (0, 1, -1), (1, 0, 0)}.

1, 1, 3, 7, 23, 74, 258, 929, 3418, 12920, 49467, 192556, 757468, 3010957, 12069935, 48741852, 198121154, 809861094, 3327311012, 13731810688, 56901053708, 236645162453, 987443318634, 4132717489200, 17344264662386, 72975042696762, 307754224161254, 1300672067496150, 5508038793509658

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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[i, -1 + j, 1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, j, -1 + 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: A339284 A057184 A148705 * A148707 A148708 A148709

Adjacent sequences: A148703 A148704 A148705 * A148707 A148708 A148709

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved