%I
%S 1,1,2,2,4,2,2,2,4,2,3,2,3,2,3,2,4,2,2,2,4,2,3,2,3,2,3,2,4,2,2,2,4,2,
%T 3,2,3,2,3,2,4,2,2,2,4,2,3,2,3,2,3,2,4,2,2,2,4,2,3,2,3,2,3,2,4,2,2,2,
%U 4,2,3,2,3,2,3,2,4,2,2,2,4,2,3,2,3,2,3,2,4,2,2,2,4,2,3,2,3,2,3,2,4,2,2,2,4
%N Number of classes of dphomogeneous spherical curves with n double points.
%C A spherical curve C is said to be dphomogeneous if the stability group of C in the group of diffeomorphisms of the sphere acts transitively on the set of double points of C. Two spherical curves belongs to the same class if there is a diffeomorphism of the sphere sending the first curve onto the second one.
%H Guy Valette, <a href="http://projecteuclid.org/euclid.bbms/1457560855">Double pointhomogeneous spherical curves</a>, Bull. Belg. Math. Soc. Simon Stevin 23 (2016), 7386.
%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,1,0,0,0,1,0,1)
%F If n>14, then a(n) = a(n12).
%F G.f.: (x^10+x^9+3*x^8+3*x^7+5*x^6+4*x^5+6*x^4+3*x^3+3*x^2+x+1) / (x^8+x^6x^21).
%e The second term of the sequence means that all double pointhomogeneous spherical curves with just one double point belong to the same orbit relatively to the group of diffeomorphisms of the sphere (it is not true for plane curves: a lemniscate of Bernoulli is not equivalent with a Pascal's limaçon).  _Guy Valette_, Feb 21 2017
%t CoefficientList[Series[(x^10 + x^9 + 3 x^8 + 3 x^7 + 5 x^6 + 4 x^5 + 6 x^4 + 3 x^3 + 3 x^2 + x + 1)/(x^8 + x^6  x^2  1), {x, 0, 120}], x] (* _Michael De Vlieger_, Feb 21 2017 *)
%K nonn,easy
%O 0,3
%A _Guy Valette_, Jun 12 2004
%E More terms from _David Wasserman_, Jun 29 2007
