A150423 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, 0, 1), (1, 0, 1), (1, 1, -1)}.

1, 2, 7, 24, 96, 390, 1640, 7003, 30629, 135960, 610766, 2762496, 12597678, 57882821, 267706394, 1243964373, 5803343475, 27181577787, 127811261317, 602994481450, 2852581142432, 13527290314262, 64302155624496, 306367818206171, 1462679856613386, 6995553173184415, 33511988966326965, 160793288870253855

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, 1 + k, -1 + n] + aux[-1 + i, j, -1 + k, -1 + n] + aux[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: A137952 A005754 A007162 * A150424 A150425 A102286

Adjacent sequences: A150420 A150421 A150422 * A150424 A150425 A150426

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved