A150538 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), (0, 1, -1), (0, 1, 1), (1, 0, 1)}.

1, 2, 7, 26, 103, 422, 1786, 7645, 33271, 146306, 648140, 2893384, 12988212, 58575492, 265345857, 1206196837, 5500661829, 25157087237, 115338984259, 530013502114, 2440558371332, 11258873388678, 52029146530007, 240811236082350, 1116177768936834, 5180510647950505, 24074102190288726, 112003280535891910

Offset

0,2

Links

Table of n, a(n) for n=0..27.

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[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, -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: A363773 A119243 A264224 * A150539 A150540 A150541

Adjacent sequences: A150535 A150536 A150537 * A150539 A150540 A150541

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved