A195197 Number of Hamiltonian cycles in the generalized Petersen Graph P(n,2).

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

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