

A225018


Number of cusps in a class of degree3n complex algebraic surfaces.


0



3, 30, 127, 301, 647, 1100, 1851, 2715, 4027, 5434, 7463, 9545, 12447, 15336, 19267, 23095, 28211, 33110, 39567, 45669, 53623, 61060, 70667, 79571, 90987, 101490, 114871, 127105, 142607, 156704, 174483, 190575, 210787, 229006, 251807, 272285, 297831, 320700
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OFFSET

1,1


COMMENTS

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.


LINKS



FORMULA

a(n) = (1/2)*(12*n^39*n^2+4*n1) if n is odd; a(n) = (1/2)*(12*n^312*n^2+7*n2) if n is even.
G.f.: x*(3+27*x+88*x^2+93*x^3+64*x^4+12*x^5+x^6)/((1x)^4*(1+x)^3). [Bruno Berselli, Apr 24 2013]
a(n) = (24*n^321*n^2+11*n(3*n^23*n+1)*(1)^n3)/4. [Bruno Berselli, Apr 24 2013]


MATHEMATICA

LinearRecurrence[{1, 3, 3, 3, 3, 1, 1}, {3, 30, 127, 301, 647, 1100, 1851}, 40] (* Bruno Berselli, Apr 24 2013 *)


PROG

(Magma) [(24*n^321*n^2+11*n(3*n^23*n+1)*(1)^n3)/4: n in [1..40]]; // Bruno Berselli, Apr 24 2013


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



