A165640 Number of distinct multisets of n integers, each of which is -2, +1, or +3, such that the sum of the members of each multiset is 3.

1, 0, 1, 1, 1, 2, 1, 1, 2, 2, 2, 2, 2, 2, 3, 3, 2, 3, 3, 3, 4, 3, 3, 4, 4, 4, 4, 4, 4, 5, 5, 4, 5, 5, 5, 6, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 6, 7, 7, 7, 8, 7, 7, 8, 8, 8, 8, 8, 8, 9, 9, 8, 9, 9, 9, 10, 9, 9, 10, 10, 10, 10, 10, 10, 11, 11, 10, 11, 11, 11, 12, 11, 11, 12, 12, 12, 12, 12, 12, 13, 13, 12

Offset: 1

Author

John W. Layman, Sep 23 2009

Keywords

• nonn

Examples

			For n=6, the multisets {-2,1,1,1,1,1}, {-2,-2,-2,3,3,3}, and no others, sum to 3, so a(6)=2.
		

Crossrefs

Cf. A008676.

Formula

Conjecture: a(n) = floor(4*(n+4)/5) - floor(2*(n+4)/3).

Empirical g.f.: -x*(x^7-x^4-x^2-1) / ((x-1)^2*(x^2+x+1)*(x^4+x^3+x^2+x+1)). - Colin Barker, Nov 06 2014