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%I #9 Feb 26 2014 08:31:51
%S 0,0,1,4,12,27,52,91,147,225,331,469,645,867,1141,1474,1875,2352,2914,
%T 3571,4332,5208,6211,7351,8640,10092,11719,13534,15552,17787,20254,
%U 22969,25947,29205,32761,36631,40833,45387,50311,55624
%N Number of distinct partitions of triangular numbers n*(n+1)/2 into 3 parts for n>=1.
%C Equals the third column in triangle A104382.
%F a(n) = round((3n^4 + 6n^3 - 33n^2 - 36n + 110)/144) (conjectured). - _Ralf Stephan_, Nov 13 2010.
%o (PARI) {a(n)=if(n<1,0,polcoeff(polcoeff( prod(i=1,n*(n+1)/2,1+y*x^i,1+x*O(x^(n*(n+1)/2))),n*(n+1)/2,x),3,y))}
%Y Cf. A000009, A104382.
%K nonn
%O 1,4
%A _Paul D. Hanna_, Mar 04 2005