login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A195197 Number of Hamiltonian cycles in the generalized Petersen Graph P(n,2). 1
3, 8, 0, 6, 7, 12, 3, 30, 0, 34, 13, 56, 3, 108, 0, 150, 19, 244, 3, 418, 0, 642, 25, 1040, 3, 1712, 0, 2726, 31, 4412, 3, 7174, 0, 11554, 37, 18696, 3, 30292, 0, 48950, 43, 79204, 3, 128202, 0, 207362, 49, 335520 (list; graph; refs; listen; history; text; internal format)
OFFSET

3,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 3..1000

A. J. Schwenk, Enumeration of Hamiltonian cycles in certain generalized Petersen graphs, J. Combin. Theory B 47 (1) (1989) 53-59.

Index entries for linear recurrences with constant coefficients, signature (0, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 0, 1).

FORMULA

G.f. -x^3*(3 +8*x -5*x^3 -4*x^4 +x^5 -5*x^6 +x^9 +2*x^10 +x^11 -3*x^2 -5*x^8)  / ( (1+x) *(x^2-x+1) *(x^4+x^2-1) *(x-1)^2 *(1+x+x^2)^2 )

MAPLE

A195197 := proc(n)

        if modp(n, 6) =0 or modp(n, 6) = 2 then

                2*(combinat[fibonacci](n/2+2)-combinat[fibonacci](n/2-2)-1) ;

        elif modp(n, 6) = 1 then

                n;

        elif modp(n, 6) = 3 then

                3;

        elif modp(n, 6) = 4 then

                n+2*(combinat[fibonacci](n/2+2)-combinat[fibonacci](n/2-2)-1) ;

        else

                0;

        end if;

end proc:

MATHEMATICA

CoefficientList[Series[-(3 + 8*x - 5*x^3 - 4*x^4 + x^5 - 5*x^6 + x^9 + 2*x^10 + x^11 - 3*x^2 - 5*x^8)/((1+x)*(x^2-x+1)*(x^4+x^2-1)*(x-1)^2*(1+x+x^2)^2), {x, 0, 60}], x] (* Vincenzo Librandi, Dec 23 2012 *)

CROSSREFS

Sequence in context: A196609 A070063 A016668 * A154462 A112255 A197417

Adjacent sequences:  A195194 A195195 A195196 * A195198 A195199 A195200

KEYWORD

nonn,easy

AUTHOR

R. J. Mathar, Sep 11 2011

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 26 10:23 EDT 2022. Contains 354879 sequences. (Running on oeis4.)