A148367 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, 1), (-1, 1, 1), (0, 1, 0), (1, -1, 0), (1, 1, -1)}.

1, 1, 2, 5, 15, 50, 184, 701, 2795, 11495, 48458, 208599, 913446, 4056442, 18230522, 82764668, 379005858, 1748636487, 8120470721, 37926160085, 178024257835, 839368322732, 3973257339484, 18874687815232, 89948704380823, 429888780149783, 2059894274722528, 9893675704123007, 47621510888750021

Offset

0,3

Links

Table of n, a(n) for n=0..28.

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, k, -1 + n] + aux[i, -1 + j, k, -1 + n] + aux[1 + i, -1 + j, -1 + k, -1 + n] + aux[1 + i, 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: A060049 A107590 A245311 * A306836 A192634 A350490

Adjacent sequences: A148364 A148365 A148366 * A148368 A148369 A148370

Keyword

nonn,walk

Author

Manuel Kauers, Nov 18 2008

Status

approved