%I #25 Sep 08 2022 08:44:32

%S 12,480,13440,382080,10859520,308651520,8772556800,249335408640,

%T 7086662123520,201418564362240,5724759747624960,162710295705845760,

%U 4624585396735180800,131440914657055211520,3735840635158368092160

%N Number of Hamiltonian cycles 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="/A003749/b003749.txt">Table of n, a(n) for n = 1..700</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_02">Index entries for linear recurrences with constant coefficients</a>, signature (28,12).

%F a(n) = 28a(n-1) + 12a(n-2), n>2.

%F G.f.: 12*x*(12*x^2-12*x-1)/(12*x^2+28*x-1). - _Colin Barker_, Aug 30 2012

%t CoefficientList[Series[12 (12 x^2 - 12 x - 1)/(12 x^2 + 28 x - 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 14 2013 *)

%o (Magma) I:=[12,480,13440]; [n le 3 select I[n] else 28*Self(n-1)+12*Self(n-2): n in [1..20]]; // _Vincenzo Librandi_, Oct 14 2013

%o (PARI) a(n)=([0,1; 12,28]^(n-1)*[12;480])[1,1] \\ _Charles R Greathouse IV_, Jun 23 2020

%K nonn,easy

%O 1,1

%A _Frans J. Faase_