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A028452
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Number of perfect matchings in graph P_{3} X P_{3} X P_{2n}.
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4
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1, 229, 117805, 64647289, 35669566217, 19690797527709, 10870506600976757, 6001202979497804657, 3313042830624031354513, 1829008840116358153050197, 1009728374600381843221483965, 557433823481589253332775648233, 307738670509229621147710358375321
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 0..300
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.
Per Hakan Lundow, Enumeration of matchings in polygraphs, 1998.
R. J. Mathar, Tilings of rectangular regions by rectangular tiles: Counts derived from transfer matrices, arXiv:1406.7788 (2014), eq (38).
J. Propp, A reciprocity theorem for domino tilings, El. J. Combin. 8 (2001) #R18
J. de Ruiter, Counting Domino Coverings and Chessboard Cycles, 2010.
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FORMULA
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From Johan de Ruiter, Jul 15 2012: (Start)
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).
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).
(End)
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CROSSREFS
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Cf. A006253, A028454, A049507.
Sequence in context: A124684 A332740 A178673 * A072020 A177826 A122269
Adjacent sequences: A028449 A028450 A028451 * A028453 A028454 A028455
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KEYWORD
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nonn
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AUTHOR
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Per H. Lundow
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STATUS
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approved
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