A165640 - OEIS

%I #8 Nov 06 2014 11:53:08

%S 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,

%T 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,

%U 10,10,10,10,10,10,11,11,10,11,11,11,12,11,11,12,12,12,12,12,12,13,13,12

%N 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.

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

%F 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

%e 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.

%Y Cf. A008676.

%K nonn

%O 1,6

%A _John W. Layman_, Sep 23 2009