A003748 - OEIS

%I #27 Sep 08 2022 08:44:32

%S 12,814,41278,2169266,113488662,5940718514,310952704838,

%T 16276223002786,851946706852182,44593472067545554,2334157405518854758,

%U 122176869250651741826,6395107433748612174582,334739295101566253176754,17521268695699930046150918,917116278846033398175880546

%N Number of 2-factors in K_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="/A003748/b003748.txt">Table of n, a(n) for n = 1..590</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_03">Index entries for linear recurrences with constant coefficients</a>, signature (47,288,-436).

%F a(1) = 12,

%F a(2) = 814,

%F a(3) = 41278, and

%F a(n) = 47a(n-1) + 288a(n-2) - 436a(n-3).

%F G.f.: -2*x*(218*x^2-125*x-6)/(436*x^3-288*x^2-47*x+1). - _Colin Barker_, Aug 30 2012

%t CoefficientList[Series[-2 (218 x^2 - 125 x - 6)/(436 x^3 - 288 x^2 - 47 x + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 14 2013 *)

%t LinearRecurrence[{47,288,-436},{12,814,41278},20] (* _Harvey P. Dale_, May 05 2022 *)

%o (Magma) I:=[12,814,41278]; [n le 3 select I[n] else 47*Self(n-1)+288*Self(n-2)-436*Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Oct 14 2013

%K nonn,easy

%O 1,1

%A _Frans J. Faase_

%E Added recurrence from Faase's web page. - _N. J. A. Sloane_, Feb 03 2009