A148774 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), (0, 1, -1), (1, -1, -1), (1, 0, 1)}.

1, 1, 3, 8, 22, 80, 265, 888, 3336, 12249, 45072, 173673, 672941, 2595981, 10244208, 41012730, 162936518, 655570981, 2678127981, 10874155875, 44444744731, 183974555899, 759720059015, 3144923360494, 13144320477323, 54991936410992, 230045973211635, 969001518828255, 4094574894059769

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, -1 + k, -1 + n] + aux[-1 + i, 1 + j, 1 + k, -1 + n] + aux[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: A361866 A148772 A148773 * A093537 A373400 A180621

Adjacent sequences: A148771 A148772 A148773 * A148775 A148776 A148777

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved