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

1,6

Links

Table of n, a(n) for n=1..92.

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

Example

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.

Sequence in context: A015718 A008350 A019556 * A082892 A025839 A053261

Adjacent sequences: A165637 A165638 A165639 * A165641 A165642 A165643

Keyword

nonn

Author

John W. Layman, Sep 23 2009

Status

approved