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A003733
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Number of spanning trees in C_5 X P_n.
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8
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5, 1805, 508805, 140503005, 38720000000, 10668237057005, 2939274449134805, 809816405722655805, 223117116976138566005, 61472262298219520000000, 16936571572967914651674005, 4666290873812984282155907805, 1285636259054921313298518442805
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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(n) = 319*a(n-1) - 12441*a(n-2) + 128319*a(n-3) - 408001*a(n-4) + 408001*a(n-5) - 128319*a(n-6) + 12441*a(n-7) - 319*a(n-8) + a(n-9). [Modified by Paul Raff, Oct 30 2009]
G.f.: -5*x *(1+x) *(x^6+41*x^5-998*x^4+2722*x^3-998*x^2+41*x+1) / ( (x-1)*(x^4-279*x^3+961*x^2-279*x+1) *(x^4-39*x^3+281*x^2-39*x+1) ).
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MAPLE
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a:= n-> (Matrix(1, 9, (i, j)-> [0, 5, 1805, 508805, 140503005][1+abs(j-5)]). Matrix(9, (i, j)-> if (i=j-1) then 1 elif j=1 then -[408001, 128319, 12441, 319, 1][1/2+abs(i-9/2)] *(-1)^i else 0 fi)^n)[1, 5]: seq(a(n), n=1..20); # Alois P. Heinz, Mar 28 2009
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MATHEMATICA
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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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