Search: id:A028468
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%I A028468
%S A028468 1,1,13,41,281,1183,6728,31529,167089,817991,4213133,21001799,
%T A028468 106912793,536948224,2720246633,13704300553,69289288909,
%U A028468 349519610713,1765722581057,8911652846951,45005025662792
%N A028468 Number of perfect matchings in graph P_{6} X P_{n}.
%D A028468 F. Faase, On the number of specific spanning subgraphs of the graphs 
               G X P_n, Ars Combin. 49 (1998), 129-154.
%D A028468 Per Hakan Lundow, "Computation of matching polynomials and the number 
               of 1-factors in polygraphs", Research report, No 12, 1996, Department 
               of Math., Umea University, Sweden.
%D A028468 R. P. Stanley, Enumerative Combinatorics I, p. 292.
%H A028468 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 A028468 F. Faase, <a href="http://www.iwriteiam.nl/counting.html">Counting Hamilton 
               cycles in product graphs</a>
%H A028468 F. Faase, <a href="http://www.iwriteiam.nl/Cresults.html">Results from 
               the counting program</a>
%H A028468 Per Hakan Lundow, <a href="http://www.theophys.kth.se/~phl/Text/1factors2.ps.gz">
               Enumeration of matchings in polygraphs</a>, 1998.
%F A028468 a(1) = 1,
%F A028468 a(2) = 13,
%F A028468 a(3) = 41,
%F A028468 a(4) = 281,
%F A028468 a(5) = 1183,
%F A028468 a(6) = 6728,
%F A028468 a(7) = 31529,
%F A028468 a(8) = 167089,
%F A028468 a(9) = 817991,
%F A028468 a(10) = 4213133,
%F A028468 a(11) = 21001799,
%F A028468 a(12) = 106912793,
%F A028468 a(13) = 536948224,
%F A028468 a(14) = 2720246633, and
%F A028468 a(n) = 40a(n-2) - 416a(n-4) + 1224a(n-6) - 1224a(n-8) + 416a(n-10) - 
               40a(n-12) + a(n-14).
%F A028468 G.f.: (1-8*x^2-2*x^3+8*x^4-x^6)/(1-x-20*x^2-10*x^3+38*x^4+10*x^5-20*x^6+x^7+x^8).
%Y A028468 Row 6 of array A099390.
%Y A028468 Sequence in context: A141970 A167240 A147247 this_sequence A146995 A102130 
               A080186
%Y A028468 Adjacent sequences: A028465 A028466 A028467 this_sequence A028469 A028470 
               A028471
%K A028468 nonn
%O A028468 0,3
%A A028468 N. J. A. Sloane (njas(AT)research.att.com), Per Hakan Lundow (phl(AT)theophys.kth.se)
%E A028468 Added recurrence from Faase's web page. - N. J. A. Sloane (njas(AT)research.att.com), 
               Feb 03 2009

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