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A003698
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Number of 2-factors in C_4 X P_n.
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1
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1, 9, 53, 341, 2169, 13825, 88093, 561357, 3577121, 22794425, 145252485, 925589701, 5898117961, 37584466929, 239498796653, 1526153708861, 9725080775409, 61970950592425, 394896331045333, 2516390514947637
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OFFSET
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1,2
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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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a(n) = 6*a(n-1) + 3*a(n-2) - 4*a(n-3), n>3.
G.f.: x*(1-x)*(1+4*x)/((1+x)*(1-7*x+4*x^2)). - Colin Barker, Aug 30 2012
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MAPLE
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seq( simplify( (-1)^n + 2^n*Chebyshev(n, 7/4) - 2^(n+1)*ChebyshevU(n-1, 7/4))/2 ), n=1..30); # G. C. Greubel, Dec 24 2019
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MATHEMATICA
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Rest@CoefficientList[Series[x*(1-x)*(1+4*x)/((1+x)*(1-7*x+4*x^2)), {x, 0, 30}], x] (* Vincenzo Librandi, Oct 13 2013 *)
Table[((-1)^n + 2^n*ChebyshevU[n, 7/4] - 2^(n+1)*ChebyshevU[n-1, 7/4])/2, {n, 30}] (* G. C. Greubel, Dec 24 2019 *)
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PROG
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(PARI) vector(30, n, ((-1)^n + 2^n*polchebyshev(n, 2, 7/4) - 2^(n+1)*polchebyshev(n-1, 2, 7/4))/2 ) \\ G. C. Greubel, Dec 24 2019
(Magma) I:=[1, 9, 53]; [n le 3 select I[n] else 6*Self(n-1) +3*Self(n-2) -4*Self(n-3): n in [1..20]]; // G. C. Greubel, Dec 24 2019
(Sage) [((-1)^n + 2^n*chebyshev_U(n, 7/4) - 2^(n+1)*chebyshev_U(n-1, 7/4))/2 for n in (1..30)] # G. C. Greubel, Dec 24 2019
(GAP) a:=[1, 9, 53];; for n in [4..30] do a[n]:=6*a[n-1]+3*a[n-2]-4*a[n-3]; od; a; # G. C. Greubel, Dec 24 2019
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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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STATUS
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approved
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