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A003761
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Number of spanning trees in D_4 X P_n.
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1
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3, 270, 20160, 1477980, 108097935, 7903526400, 577834413429, 42245731959480, 3088601154192960, 225808743709815750, 16508958287605688193, 1206975861055570636800, 88242438021480689844999, 6451436286916714206370530, 471666820375043557337304000
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OFFSET
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1,1
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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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a(1) = 3,
a(2) = 270,
a(3) = 20160,
a(4) = 1477980,
a(5) = 108097935,
a(6) = 7903526400,
a(7) = 577834413429,
a(8) = 42245731959480 and
a(n) = 90*a(n-1) - 1313*a(n-2) + 5850*a(n-3) - 9828*a(n-4) + 5850*a(n-5) - 1313*a(n-6) + 90*a(n-7) - a(n-8).
G.f.: 3*x*(x^6 -67*x^4 +180*x^3 -67*x^2 +1) / (x^8 -90*x^7 +1313*x^6 -5850*x^5 +9828*x^4 -5850*x^3 +1313*x^2 -90*x +1). - Paul Raff, Mar 06 2009
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MATHEMATICA
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CoefficientList[Series[3 (x^6 - 67 x^4 + 180 x^3 - 67 x^2 + 1)/(x^8 - 90 x^7 + 1313 x^6 - 5850 x^5 + 9828 x^4 - 5850 x^3 + 1313 x^2 - 90 x + 1), {x, 0, 33}], x] (* Vincenzo Librandi, Aug 03 2015 *)
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PROG
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(Magma) I:=[3, 270, 20160, 1477980, 108097935, 7903526400, 577834413429, 42245731959480]; [n le 8 select I[n] else 90*Self(n-1)-1313*Self(n-2)+5850*Self(n-3)-9828*Self(n-4)+5850*Self(n-5)-1313*Self(n-6)+90*Self(n-7)-Self(n-8): n in [1..20]]; // Vincenzo Librandi, Aug 03 2015
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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