%I #26 Jun 23 2020 09:42:40

%S 1,11,81,666,5431,44466,364061,2981201,24412606,199912706,1637069691,

%T 13405842666,109779463516,898976005896,7361648869421,60284005131851,

%U 493661316969811,4042556485091321,33104199931650186

%N Number of 2-factors in C_5 X P_n.

%D F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.

%H Vincenzo Librandi, <a href="/A003730/b003730.txt">Table of n, a(n) for n = 1..1000</a>

%H F. Faase, <a href="http://www.iwriteiam.nl/Cpaper.zip">On the number of specific spanning subgraphs of the graphs G X P_n</a>, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154.

%H F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamiltonian cycles in product graphs</a>

%H F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from the counting program</a>

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (9,-4,-22,3).

%F a(n) = 9a(n-1) - 4a(n-2) - 22a(n-3) + 3a(n-4), n>4.

%F G.f.: -x*(3*x^3-14*x^2+2*x+1)/(3*x^4-22*x^3-4*x^2+9*x-1). - _Colin Barker_, Aug 30 2012

%t CoefficientList[Series[-(3 x^3 - 14 x^2 + 2 x + 1)/(3 x^4 - 22 x^3 - 4 x^2 + 9 x - 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 13 2013 *)

%t LinearRecurrence[{9,-4,-22,3},{1,11,81,666},30] (* _Harvey P. Dale_, Sep 23 2016 *)

%o (PARI) a(n)=([0,1,0,0; 0,0,1,0; 0,0,0,1; 3,-22,-4,9]^(n-1)*[1;11;81;666])[1,1] \\ _Charles R Greathouse IV_, Jun 23 2020

%K nonn,easy

%O 1,2

%A _Frans J. Faase_