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%I #18 Jul 04 2021 03:00:19
%S 0,0,0,0,0,0,0,0,0,0,1,0,1,1,1,1,3,1,3,3,3,3,6,3,6,6,6,6,10,6,10,10,
%T 10,10,15,10,15,15,15,15,21,15,21,21,21,21,28,21,28,28,28,28,36,28,36,
%U 36,36,36,45,36,45,45,45,45,55,45,55,55,55,55,66,55,66,66,66,66,78,66,78,78,78,78,91
%N Number of integer-sided triangles with sides a,b,c, a<b<c, a+b+c=n such that c - b < b - a.
%H Vincenzo Librandi, <a href="/A024163/b024163.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_11">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,1,0,-1,1,0,-1,-1,0,1).
%F G.f.: x^11/((1-x^2)*(1-x^3)*(1-x^6)). - _Tani Akinari_, Oct 27 2014
%e 2,4,5 for n=11 is the smallest such triangle.
%t CoefficientList[Series[x^10/((1-x^2)(1-x^3)(1-x^6)), {x, 0, 100}], x] (* _Vincenzo Librandi_, Oct 28 2014 *)
%o (PARI) concat(vector(11,i,0), Vec(1/(1-x^2)/(1-x^3)/(1-x^6)+O(x^99))) \\ _Charles R Greathouse IV_, Oct 28 2014
%o (Sage)
%o def A024163_list(prec):
%o P.<x> = PowerSeriesRing(QQ, prec)
%o return P( x^11/((1-x^2)*(1-x^3)*(1-x^6)) ).list()
%o a=A024163_list(100); a[1:] # _G. C. Greubel_, Jul 03 2021
%o (Magma)
%o R<x>:=PowerSeriesRing(Rationals(), 100);
%o [0,0,0,0,0,0,0,0,0,0] cat Coefficients(R!( x^11/((1-x^2)*(1-x^3)*(1-x^6)) )); // _G. C. Greubel_, Jul 03 2021
%Y Cf. A024165.
%K nonn,easy
%O 1,17
%A _Clark Kimberling_
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