A165640 - OEIS

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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

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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.