A148567 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, 0), (1, 0, -1), (1, 1, 0)}.

1, 1, 3, 6, 19, 48, 163, 458, 1605, 4837, 17348, 54662, 199115, 648801, 2391554, 7986126, 29705879, 101170951, 379067774, 1311200087, 4941974339, 17317592643, 65592787213, 232321727590, 883623114005, 3158597045417, 12056381659368, 43435180563827, 166305377501064, 603267534346636, 2316036020003194

Offset

0,3

Links

Table of n, a(n) for n=0..30.

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, k, -1 + n] + aux[-1 + i, j, 1 + k, -1 + n] + aux[1 + i, j, 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: A007098 A226322 A148566 * A148568 A003162 A179277

Adjacent sequences: A148564 A148565 A148566 * A148568 A148569 A148570

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved