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%I #6 Jun 13 2015 00:51:03
%S 0,1,2,9,17,37,63,108,165,252,358,506,684,917,1192,1539,1941,2433,
%T 2997,3670,4433,5328,6332,7492,8784,10257,11886,13725,15745,18005,
%U 20475,23216,26197,29484,33042,36942,41148,45733,50660,56007,61733,67921,74529,81642
%N G.f.: (x+4*x^3+x^5)/((1-x)^2*(1-x^2)^2*(1-x^3)).
%D H. Gupta, Magic partitions, I, Math. Student 45 (1977), no. 3, 58-62.
%H <a href="/index/Rec#order_09">Index entries for linear recurrences with constant coefficients</a>, signature (2, 1, -3, -1, 1, 3, -1, -2, 1).
%F a(0)=0, a(1)=1, a(2)=2, a(3)=9, a(4)=17, a(5)=37, a(6)=63, a(7)=108, a(8)=165, a(n)=2*a(n-1)+a(n-2)-3*a(n-3)-a(n-4)+a(n-5)+3*a(n-6)- a(n-7)-2*a(n-8)+ a(n-9). - _Harvey P. Dale_, May 01 2015
%t CoefficientList[Series[(x+4x^3+x^5)/((1-x)^2(1-x^2)^2(1-x^3)),{x,0,50}],x] (* or *) LinearRecurrence[{2,1,-3,-1,1,3,-1,-2,1},{0,1,2,9,17,37,63,108,165},50] (* _Harvey P. Dale_, May 01 2015 *)
%Y Cf. A083708, A083709.
%K nonn
%O 0,3
%A _N. J. A. Sloane_, Jun 15 2003
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