A150337 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, -1, 1), (1, 0, 0), (1, 1, 0)}.

1, 2, 7, 23, 86, 324, 1299, 5220, 21719, 90339, 384266, 1636936, 7082536, 30702416, 134564005, 590760674, 2614779499, 11592637398, 51721170509, 231138434046, 1038072189221, 4669365170633, 21086844125900, 95366701040696, 432706722580237, 1965994726429393, 8956638737150482, 40856306161760969

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, k, -1 + n] + aux[-1 + 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: A151292 A179533 A352173 * A150338 A150339 A150340

Adjacent sequences: A150334 A150335 A150336 * A150338 A150339 A150340

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved