A148643 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, 1), (-1, 1, 0), (1, 0, 0), (1, 1, -1)}.

1, 1, 3, 6, 23, 59, 242, 710, 3065, 9745, 43180, 145334, 657471, 2303819, 10560958, 38192920, 177000421, 655911820, 3063612225, 11584103157, 54465884875, 209362835421, 989410879714, 3857103432676, 18308370061781, 72228022261289, 344064913864890, 1371579311929437, 6554070713864930

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, -1 + j, 1 + k, -1 + n] + aux[-1 + i, j, k, -1 + n] + aux[1 + i, -1 + j, k, -1 + n] + aux[1 + i, j, -1 + 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: A176424 A341549 A151443 * A240646 A148644 A148645

Adjacent sequences: A148640 A148641 A148642 * A148644 A148645 A148646

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved