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%I #28 Sep 08 2022 08:44:32
%S 29,1189,49401,2053641,85373589,3549138989,147544320241,6133692298001,
%T 254989017189389,10600368542888629,440677071050573801,
%U 18319766917914642201,761586844367955639429,31660584117320436988989,1316189472103884945976801,54716448693989525183595041
%N Number of perfect matchings (or domino tilings) in W_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="/A003735/b003735.txt">Table of n, a(n) for n = 1..600</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_04">Index entries for linear recurrences with constant coefficients</a>, signature (44,-102,44,-1).
%F a(n) = 44a(n-1) - 102a(n-2) + 44a(n-3) - a(n-4), n>4.
%F G.f.: -x*(x^3-43*x^2+87*x-29)/(x^4-44*x^3+102*x^2-44*x+1). - _Colin Barker_, Aug 30 2012
%t CoefficientList[Series[-(x^3 - 43 x^2 + 87 x - 29)/(x^4 - 44 x^3 + 102 x^2 - 44 x + 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Oct 14 2013 *)
%t LinearRecurrence[{44,-102,44,-1},{29,1189,49401,2053641},20] (* _Harvey P. Dale_, Jul 19 2018 *)
%o (Magma) I:=[29,1189,49401,2053641]; [n le 4 select I[n] else 44*Self(n-1)-102*Self(n-2)+44*Self(n-3)-Self(n-4): n in [1..20]]; // _Vincenzo Librandi_, Oct 14 2013
%o (PARI) Vec(-x*(x^3-43*x^2+87*x-29)/(x^4-44*x^3+102*x^2-44*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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