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A081017
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a(n) = Lucas(4n+1) - 1, or 5*Fibonacci(2n)*Fibonacci(2n+1).
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3
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0, 10, 75, 520, 3570, 24475, 167760, 1149850, 7881195, 54018520, 370248450, 2537720635, 17393796000, 119218851370, 817138163595, 5600748293800, 38388099893010, 263115950957275, 1803423556807920, 12360848946698170
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OFFSET
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0,2
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REFERENCES
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Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75.
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LINKS
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FORMULA
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a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3).
G.f.: 5*x*(2-x)/((1-x)*(1-7*x+x^2)). - Colin Barker, Apr 16 2012
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MAPLE
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with(combinat): option remember: if n=0 then RETURN(2) fi: if n=1 then RETURN(1) fi: luc(n-1)+luc(n-2): end: for n from 0 to 25 do printf(`%d, `, luc(4*n+1)-1) od: # James A. Sellers, Mar 03 2003
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MATHEMATICA
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LucasL[4*Range[0, 20]+1]-1 (* or *) LinearRecurrence[{8, -8, 1}, {0, 10, 75}, 20] (* Harvey P. Dale, Mar 02 2015 *)
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PROG
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(PARI) vector(20, n, n--; f=fibonacci; f(4*n+2)+f(4*n)-1) \\ G. C. Greubel, Jul 14 2019
(Magma) [Lucas(4*n+1) -1: n in [0..20]]; // G. C. Greubel, Jul 14 2019
(Sage) [lucas_number2(4*n+1, 1, -1) - 1 for n in (0..20)] # G. C. Greubel, Jul 14 2019
(GAP) List([0..20], n-> Lucas(1, -1, 4*n+1)[2] -1 ); # G. C. Greubel, Jul 14 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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EXTENSIONS
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STATUS
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approved
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