login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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

Table of n, a(n) for n=0..104.

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 lima├žon). - 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

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified May 19 02:29 EDT 2019. Contains 323377 sequences. (Running on oeis4.)