

A094818


Number of classes of dphomogeneous spherical curves with n double points.


0



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, 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, 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
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OFFSET

0,3


COMMENTS

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.


LINKS

Table of n, a(n) for n=0..104.
Guy Valette, Double pointhomogeneous spherical curves, Bull. Belg. Math. Soc. Simon Stevin 23 (2016), 7386.
Index entries for linear recurrences with constant coefficients, signature (0,1,0,0,0,1,0,1)


FORMULA

If n>14, then a(n) = a(n12).
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).


EXAMPLE

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


MATHEMATICA

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 *)


CROSSREFS

Sequence in context: A289827 A092188 A097884 * A114233 A279047 A063086
Adjacent sequences: A094815 A094816 A094817 * A094819 A094820 A094821


KEYWORD

nonn


AUTHOR

Guy Valette, Jun 12 2004


EXTENSIONS

More terms from David Wasserman, Jun 29 2007


STATUS

approved



