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 A195197 Number of Hamiltonian cycles in the generalized Petersen Graph P(n,2). 1

%I

%S 3,8,0,6,7,12,3,30,0,34,13,56,3,108,0,150,19,244,3,418,0,642,25,1040,

%T 3,1712,0,2726,31,4412,3,7174,0,11554,37,18696,3,30292,0,48950,43,

%U 79204,3,128202,0,207362,49,335520

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

%H Vincenzo Librandi, <a href="/A195197/b195197.txt">Table of n, a(n) for n = 3..1000</a>

%H A. J. Schwenk, <a href="http://dx.doi.org/10.1016/0095-8956(89)90064-6">Enumeration of Hamiltonian cycles in certain generalized Petersen graphs</a>, J. Combin. Theory B 47 (1) (1989) 53-59.

%H <a href="/index/Rec#order_13">Index entries for linear recurrences with constant coefficients</a>, signature (0, 1, 1, 1, -1, 1, -1, -1, -1, -1, 1, 0, 1).

%F 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 )

%p A195197 := proc(n)

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

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

%p elif modp(n,6) = 1 then

%p n;

%p elif modp(n,6) = 3 then

%p 3;

%p elif modp(n,6) = 4 then

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

%p else

%p 0;

%p end if;

%p end proc:

%t 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 *)

%K nonn,easy

%O 3,1

%A _R. J. Mathar_, Sep 11 2011

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Last modified August 7 23:50 EDT 2022. Contains 355995 sequences. (Running on oeis4.)