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%I #16 Sep 08 2022 08:46:04
%S 3,30,127,301,647,1100,1851,2715,4027,5434,7463,9545,12447,15336,
%T 19267,23095,28211,33110,39567,45669,53623,61060,70667,79571,90987,
%U 101490,114871,127105,142607,156704,174483,190575,210787,229006,251807,272285,297831,320700
%N Number of cusps in a class of degree-3n complex algebraic surfaces.
%C The sequence gives the number of cusps of a family of algebraic surfaces with degrees 3n. They are obtained by using Belyi polynomials in combination with a class of complex polynomials related to the generation of surfaces with many ordinary double points.
%H J. G. Escudero, <a href="http://dx.doi.org/10.1016/j.cam.2013.03.045">Hypersurfaces with many Aj-singularities: Explicit constructions</a>, Journal of Computational and Applied Mathematics (2013)
%H J. G. Escudero, <a href="http://arxiv.org/abs/1302.6747">On a family of complex algebraic surfaces of degree 3n</a>, 2013, arXiv:1302.6747 [math.AG]
%H <a href="/index/Rec#order_07">Index entries for linear recurrences with constant coefficients</a>, signature (1,3,-3,-3,3,1,-1)
%F a(n) = (1/2)*(12*n^3-9*n^2+4*n-1) if n is odd; a(n) = (1/2)*(12*n^3-12*n^2+7*n-2) if n is even.
%F G.f.: x*(3+27*x+88*x^2+93*x^3+64*x^4+12*x^5+x^6)/((1-x)^4*(1+x)^3). [_Bruno Berselli_, Apr 24 2013]
%F a(n) = (24*n^3-21*n^2+11*n-(3*n^2-3*n+1)*(-1)^n-3)/4. [_Bruno Berselli_, Apr 24 2013]
%t LinearRecurrence[{1, 3, -3, -3, 3, 1, -1}, {3, 30, 127, 301, 647, 1100, 1851}, 40] (* _Bruno Berselli_, Apr 24 2013 *)
%o (Magma) [(24*n^3-21*n^2+11*n-(3*n^2-3*n+1)*(-1)^n-3)/4: n in [1..40]]; // _Bruno Berselli_, Apr 24 2013
%K nonn,easy
%O 1,1
%A _Juan G. Escudero_, Apr 24 2013
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