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%I #28 Sep 08 2022 08:44:32
%S 56,4181,313501,23508376,1762814681,132187592681,9912306636376,
%T 743290810135501,55736898453526181,4179524093204328056,
%U 313408570091871078001,23501463232797126522001,1762296333889692618072056,132148723578494149228882181,9909391972053171499548091501
%N Number of perfect matchings (or domino tilings) in K_5 X P_2n.
%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="/A003747/b003747.txt">Table of n, a(n) for n = 1..500</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/Do#domino">Index entries for sequences related to dominoes</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (76,-76,1).
%F a(n) = 76*a(n-1) - 76*a(n-2) + a(n-3), n > 3.
%F G.f.: -x*(x^2-75*x+56)/((x-1)*(x^2-75*x+1)). - _Colin Barker_, Aug 30 2012
%t CoefficientList[Series[-(x^2 - 75 x + 56)/((x - 1) (x^2 - 75 x + 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 14 2013 *)
%o (Magma) I:=[56,4181,313501]; [n le 3 select I[n] else 76*Self(n-1)-76*Self(n-2)+Self(n-3): n in [1..20]]; // _Vincenzo Librandi_, Oct 14 2013
%o (PARI) Vec(-x*(x^2-75*x+56)/((x-1)*(x^2-75*x+1))+O(x^99)) \\ _Charles R Greathouse IV_, Jun 23 2020
%K nonn,easy
%O 1,1
%A _Frans J. Faase_
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