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%I #26 Jul 10 2023 08:26:48
%S 1,229,117805,64647289,35669566217,19690797527709,10870506600976757,
%T 6001202979497804657,3313042830624031354513,1829008840116358153050197,
%U 1009728374600381843221483965,557433823481589253332775648233,307738670509229621147710358375321
%N Number of perfect matchings in graph P_{3} X P_{3} X P_{2n}.
%C Also the number of tilings of a 3 x 3 x 2n box with 1 x 1 x 2 bricks. - _Johan de Ruiter_, Jul 15 2012
%H Alois P. Heinz, <a href="/A028452/b028452.txt">Table of n, a(n) for n = 0..300</a>
%H Per Hakan Lundow, <a href="https://web.archive.org/web/20220127062648/http://www.theophys.kth.se/~phl/Text/1factors.pdf">Computation of matching polynomials and the number of 1-factors in polygraphs</a>, Research report, No 12, 1996, Department of Math., Umea University, Sweden.
%H Per Hakan Lundow, <a href="https://web.archive.org/web/20171118074340/http://www.theophys.kth.se/~phl/Text/1factors2.pdf">Enumeration of matchings in polygraphs</a>, 1998.
%H R. J. Mathar, <a href="https://arxiv.org/abs/1406.7788">Tilings of rectangular regions by rectangular tiles: Counts derived from transfer matrices</a>, arXiv:1406.7788 [math.CO], (2014), eq (38).
%H James Propp, <a href="https://doi.org/10.37236/1562">A reciprocity theorem for domino tilings</a>, El. J. Combin. 8 (2001) #R18.
%H J. de Ruiter, <a href="http://www.math.leidenuniv.nl/~jruiter/CountingDominoCoveringsAndChessboardCycles.pdf">Counting Domino Coverings and Chessboard Cycles</a>, 2010. [Broken link]
%F From _Johan de Ruiter_, Jul 15 2012: (Start)
%F a(n) = 679a(n-1) -76177a(n-2) +3519127a(n-3) -85911555a(n-4) +1235863045a(n-5) -11123194131a(n-6) +65256474997a(n-7) -257866595482a(n-8) +705239311926a(n-9) -1363115167354a(n-10) +1888426032982a(n-11) -1888426032982a(n-12) +1363115167354a(n-13) -705239311926a(n-14) +257866595482a(n-15) -65256474997a(n-16) +11123194131a(n-17) -1235863045a(n-18) +85911555a(n-19) -3519127a(n-20) +76177a(n-21) -679a(n-22) +a(n-23).
%F G.f.: (x^18 -446x^17 +36701x^16 -1267416x^15 +22828288x^14 -235207768x^13 +1443564488x^12 -5338083112x^11 +11818867674x^10 -15460884436x^9 +11818867674x^8 -5338083112x^7 +1443564488x^6 -235207768x^5 +22828288x^4 -1267416x^3 +36701x^2 -446x +1)/(-x^19 +675x^18 -73471x^17 +3221189x^16 -72583272x^15 +925908264x^14 -6971103216x^13 +31523058272x^12 -86171526770x^11 +142604534086x^10 -142604534086x^9 +86171526770x^8 -31523058272x^7 +6971103216x^6 -925908264x^5 +72583272x^4 -3221189x^3 +73471x^2 -675x +1).
%F (End)
%Y Cf. A006253, A028454, A049507.
%K nonn
%O 0,2
%A _Per H. Lundow_
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