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%I #8 Jun 13 2015 00:52:02
%S 1,3,8,12,27,27,64,48,125,75,216,108,343,147,512,192,729,243,1000,300,
%T 1331,363,1728,432,2197,507,2744,588,3375,675,4096,768,4913,867
%N Integers when g2^3-27*g3^2=0 in cubic polynomials of the form: w^2=4*x^3-g2*x-g3.
%C When the elliptic term: j=g2^3/(g2^3-27*g3^2) is singular and g2 and g3 are both integers.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-6,0,4,0,-1).
%F a(n) = If 3*n^(2/3) is an integer then {n,3*n^(2/3)}
%F a(n) = (n^3+6*n^2+12*n+8)/8 for n even. a(n) = (3*n^2+6*n+3)/4 for n odd. G.f.: -(3*x^5-x^4-4*x^2-3*x-1) / ((x-1)^4*(x+1)^4). - _Colin Barker_, Mar 15 2013
%t a = Flatten[Table[If[IntegerQ[3*n^(2/3)] == True, {n, 3*n^(2/3)}, {}], {n, 1, 5000}]]
%K nonn,uned,easy
%O 0,2
%A _Roger L. Bagula_, Feb 18 2006
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