A148363 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, 0, 0), (0, 0, 1), (1, -1, 1), (1, 1, -1)}.

1, 1, 2, 5, 15, 47, 153, 512, 1764, 6205, 22178, 80250, 293392, 1082150, 4021993, 15045305, 56589991, 213868391, 811675055, 3091968776, 11817335422, 45297815514, 174089982422, 670649127978, 2589073468862, 10014616679695, 38805067344637, 150605089773350, 585368329010851, 2278268666376329

Offset

0,3

Links

Table of n, a(n) for n=0..29.

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, 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: A151280 A149914 A071735 * A365267 A350434 A364161

Adjacent sequences: A148360 A148361 A148362 * A148364 A148365 A148366

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved