Search: id:A003775
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%I A003775
%S A003775 1,8,95,1183,14824,185921,2332097,29253160,366944287,4602858719,
%T A003775 57737128904,724240365697,9084693297025,113956161827912,
%U A003775 1429438110270431,17930520634652959,224916047725262248
%N A003775 Number of perfect matchings (or domino tilings) in P_5 X P_2n.
%D A003775 F. Faase, On the number of specific spanning subgraphs of the graphs 
               G X P_n, Ars Combin. 49 (1998), 129-154.
%D A003775 R. P. Stanley, Enumerative Combinatorics I, p. 292.
%H A003775 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 A003775 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton 
               cycles in product graphs</a>
%H A003775 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from 
               the counting program</a>
%H A003775 F. Faase, <a href="http://home.wxs.nl/~faase009/counting.html">Counting 
               Hamilton cycles in product graphs</a>
%H A003775 James A. Sellers, <a href="http://www.cs.uwaterloo.ca/journals/JIS/index.html">
               Domino Tilings and Products of Fibonacci and Pell Numbers</a>, Journal 
               of Integer Sequences, Vol. 5 (2002), Article 02.1.2
%H A003775 <a href="Sindx_Do.html#domino">Index entries for sequences related to 
               dominoes</a>
%F A003775 If b(n) denotes the number of perfect matchings (or domino tilings) in 
               P_5 X P_n we have:
%F A003775 b(1) = 0,
%F A003775 b(2) = 8,
%F A003775 b(3) = 0,
%F A003775 b(4) = 95,
%F A003775 b(5) = 0,
%F A003775 b(6) = 1183,
%F A003775 b(7) = 0,
%F A003775 b(8) = 14824 and
%F A003775 b(n) = 15b(n-2) - 32b(n-4) + 15b(n-6) - b(n-8).
%F A003775 G.f.: (1-7*x+7*x^2-x^3)/(1-15*x+32*x^2-15*x^3+x^4).
%F A003775 Let M be the 4 X 4 matrix |1 0 2 8 | 0 1 0 2 | 2 1 5 21| 1 1 1 8 |; then 
               a(n) = M^n(4, 4). - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Aug 
               08, 2003
%F A003775 Lim_{n -> Inf} a(n)/a(n-1) = (3 + Sqrt(5))*(5 + Sqrt(21))/4 = 12.54375443458... 
               - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Jun 13 = 2005.
%Y A003775 Row 5 of array A099390.
%Y A003775 Sequence in context: A010565 A080208 A099298 this_sequence A121785 A116144 
               A074114
%Y A003775 Adjacent sequences: A003772 A003773 A003774 this_sequence A003776 A003777 
               A003778
%K A003775 nonn
%O A003775 0,2
%A A003775 Frans Faase (Frans_LiXia(AT)wxs.nl)
%E A003775 Added recurrence from Faase's web page. - N. J. A. Sloane (njas(AT)research.att.com), 
               Feb 03 2009

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