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 A028469 Number of perfect matchings in graph P_{7} X P_{2n}. 6
 1, 21, 781, 31529, 1292697, 53175517, 2188978117, 90124167441, 3710708201969, 152783289861989, 6290652543875133, 259009513044645817, 10664383939345916681, 439092316687230373293, 18079062471131097321077 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154. LINKS Alois P. Heinz, Table of n, a(n) for n = 0..500 F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Preliminary version of paper that appeared in Ars Combin. 49 (1998), 129-154. F. Faase, Results from the counting program 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, Paving Rectangular Regions with Rectangular Tiles: Tatami and Non-Tatami Tilings, arXiv:1311.6135 [math.CO], Table 6. FORMULA G.f.: (-x^7 +35*x^6 -277*x^5 +727*x^4 -727*x^3 +277*x^2 -35*x +1) / (x^8 -56*x^7 +672*x^6 -2632*x^5 +4094*x^4 -2632*x^3 +672*x^2 -56*x +1). (Faase:) If b(n) denotes the number of perfect matchings in P_7 X P_n we have: b(1) = 0, b(2) = 21, b(3) = 0, b(4) = 781, b(5) = 0, b(6) = 31529, b(7) = 0, b(8) = 1292697, b(9) = 0, b(10) = 53175517, b(11) = 0, b(12) = 2188978117, b(13) = 0, b(14) = 90124167441, b(15) = 0, b(16) = 3710708201969, and b(n) = 56b(n-2) - 672b(n-4) + 2632b(n-6) - 4094b(n-8) + 2632b(n-10) - 672b(n-12) + 56b(n-14) - b(n-16). MATHEMATICA a[n_] := Product[2(2+Cos[k Pi/4]+Cos[2j Pi/(2n+1)]), {k, 1, 3}, {j, 1, n}] // Round; Table[a[n], {n, 0, 14}] (* Jean-François Alcover, Aug 20 2018 *) CROSSREFS Row 7 of array A099390. Sequence in context: A012850 A012645 A220069 * A295845 A119414 A012819 Adjacent sequences:  A028466 A028467 A028468 * A028470 A028471 A028472 KEYWORD nonn AUTHOR EXTENSIONS Added recurrence from Faase's web page. - N. J. A. Sloane, Feb 03 2009 STATUS approved

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Last modified February 20 15:10 EST 2019. Contains 320337 sequences. (Running on oeis4.)