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 A094818 Number of classes of dp-homogeneous 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS A spherical curve C is said to be dp-homogeneous 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 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) 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). EXAMPLE 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 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: A092188 A340675 A097884 * A114233 A279047 A063086 Adjacent sequences:  A094815 A094816 A094817 * A094819 A094820 A094821 KEYWORD nonn,easy AUTHOR Guy Valette, Jun 12 2004 EXTENSIONS More terms from David Wasserman, Jun 29 2007 STATUS approved

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Last modified July 28 18:58 EDT 2021. Contains 346335 sequences. (Running on oeis4.)