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A028469
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Number of perfect matchings in graph P_{7} X P_{2n}.
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8
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1, 21, 781, 31529, 1292697, 53175517, 2188978117, 90124167441, 3710708201969, 152783289861989, 6290652543875133, 259009513044645817, 10664383939345916681, 439092316687230373293, 18079062471131097321077
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OFFSET
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0,2
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REFERENCES
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F. Faase, On the number of specific spanning subgraphs of the graphs G X P_n, Ars Combin. 49 (1998), 129-154.
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LINKS
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FORMULA
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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).
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MATHEMATICA
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a[n_] := Product[2(2+Cos[k Pi/4]+Cos[2j Pi/(2n+1)]), {k, 1, 3}, {j, 1, n}] // Round;
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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