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A003741 Number of perfect matchings (or domino tilings) in O_5 X P_2n. 1

%I

%S 40,2197,121735,6748096,374079619,20737143595,1149566489968,

%T 63726386332735,3532681575875629,195834721732832344,

%U 10856126548559080585,601810968956118729913,33361479413223474759160,1849398508920455533993789,102521677843870104359906191,5683304262020707489694083600

%N Number of perfect matchings (or domino tilings) in O_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="/A003741/b003741.txt">Table of n, a(n) for n = 1..580</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">Index entries for linear recurrences with constant coefficients</a>, signature (65,-548,995,-548,65,-1).

%F If b(n) denotes the number of perfect matchings (or domino tilings) in O_5 X P_n we have:

%F b(1) = 0,

%F b(2) = 40,

%F b(3) = 0,

%F b(4) = 2197,

%F b(5) = 0,

%F b(6) = 121735,

%F b(7) = 0,

%F b(8) = 6748096,

%F b(9) = 0,

%F b(10) = 374079619,

%F b(11) = 0,

%F b(12) = 20737143595, and

%F b(n) = 65b(n-2) - 548b(n-4) + 995b(n-6) - 548b(n-8) + 65b(n-10) - b(n-12).

%F G.f.: -x*(x^5 -64*x^4 +523*x^3 -850*x^2 +403*x -40)/(x^6 -65*x^5 +548*x^4 -995*x^3 +548*x^2 -65*x +1). [_Colin Barker_, Aug 31 2012]

%t CoefficientList[Series[-(x^5 - 64 x^4 + 523 x^3 - 850 x^2 + 403 x - 40)/(x^6 - 65 x^5 + 548 x^4 - 995 x^3 + 548 x^2 - 65 x + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 14 2013 *)

%o (MAGMA) I:=[40,2197,121735,6748096,374079619, 20737143595]; [n le 6 select I[n] else 65*Self(n-1)-548*Self(n-2)+995*Self(n-3)-548*Self(n-4)+65*Self(n-5)-Self(n-6): 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

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Last modified November 13 20:57 EST 2019. Contains 329106 sequences. (Running on oeis4.)