A150387 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, -1, 0), (-1, 1, 1), (1, 0, 1), (1, 1, 0)}.

1, 2, 7, 23, 100, 368, 1710, 6716, 31823, 130061, 623003, 2611508, 12616721, 53820289, 261699739, 1131097502, 5525211564, 24129146559, 118255755796, 520778209686, 2558745315274, 11346116005601, 55860667523716, 249129364575265, 1228616735554889, 5506312402878732, 27193271314477361, 122388911479518502

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, -1 + j, k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 1 + 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: A150385 A047066 A150386 * A265797 A150388 A372194

Adjacent sequences: A150384 A150385 A150386 * A150388 A150389 A150390

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved