A094818 Number of classes of dp-homogeneous spherical curves with n double points.
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
Offset: 0
Examples
The second term of the sequence means that all double point-homogeneous 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
Links
- Guy Valette, Double point-homogeneous spherical curves, Bull. Belg. Math. Soc. Simon Stevin 23 (2016), 73-86.
- Index entries for linear recurrences with constant coefficients, signature (0,-1,0,0,0,1,0,1)
Programs
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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 *)
Formula
If n>14, then a(n) = a(n-12).
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^6-x^2-1).
Extensions
More terms from David Wasserman, Jun 29 2007
Comments