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A003753
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Number of spanning trees in C_4 X P_n.
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7
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4, 384, 31500, 2558976, 207746836, 16864848000, 1369080572444, 111141302329344, 9022397309950500, 732433860440996736, 59458627396289740076, 4826822683620921984000, 391839136544897998002484, 31809312044806091140235904, 2582264604005182130741437500
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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) = 4,
a(2) = 384,
a(3) = 31500,
a(4) = 2558976,
a(5) = 207746836,
a(6) = 16864848000 and
a(n) = 90a(n-1) - 735a(n-2) + 1548a(n-3) - 735a(n-4) + 90a(n-5) - a(n-6).
G.f.: 4x(x^4+6x^3-30x^2+6x+1)/(x^6-90x^5+735x^4-1548x^3+735x^2-90x+1). [Paul Raff, Mar 06 2009]
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MAPLE
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a:= n-> (Matrix([[4, 0, -4, -384, -31500, -2558976]]). Matrix(6, (i, j)-> if (i=j-1) then 1 elif j=1 then [90, -735, 1548, -735, 90, -1][i] else 0 fi)^(n-1))[1, 1]; seq(a(n), n=1..20); # Alois P. Heinz, Aug 01 2008
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MATHEMATICA
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a[n_] := (Sqrt[2]/3)*Sinh[n*ArcCosh[3]]*Sinh[n*ArcCosh[7]/2]^2 // Round; Array[a, 20] (* Jean-François Alcover, Jan 31 2016 *)
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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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