A148381 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, 1, -1), (0, 0, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 2, 5, 16, 48, 175, 619, 2380, 9171, 36721, 148656, 615159, 2571205, 10910476, 46683700, 201929895, 879826156, 3863795243, 17077106109, 75933757691, 339480057377, 1525266820258, 6883909361806, 31199950816510, 141945393542533, 648110580747881, 2968934724347998, 13642293546335759

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, 1 + j, -1 + k, -1 + n] + aux[i, j, -1 + k, -1 + n] + aux[1 + i, -1 + 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: A148380 A210696 A005497 * A334293 A278274 A148382

Adjacent sequences: A148378 A148379 A148380 * A148382 A148383 A148384

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved