This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A165640 #8 Nov 06 2014 11:53:08
%S A165640 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 A165640 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 A165640 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 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.
%F A165640 Conjecture: a(n) = floor(4*(n+4)/5) - floor(2*(n+4)/3).
%F A165640 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 A165640 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 A165640 Cf. A008676.
%K A165640 nonn
%O A165640 1,6
%A A165640 _John W. Layman_, Sep 23 2009