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A081067
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Lucas(4n+2)+2, or 5*Fibonacci(2n+1)^2.
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3
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5, 20, 125, 845, 5780, 39605, 271445, 1860500, 12752045, 87403805, 599074580, 4106118245, 28143753125, 192900153620, 1322157322205, 9062201101805, 62113250390420, 425730551631125, 2918000611027445, 20000273725560980
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OFFSET
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0,1
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COMMENTS
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a(n) is the square of limit of (G(j+2n-1) + G(j-2n+1))/G(j) as j -> infinity, where G(n) is any sequence of the form G(n+1) = G(n) + G(n-1), with any starting values, including non-integer values. G(n) includes Lucas and Fibonacci. Compare with A005248 for even number offsets from j in any such G(n). - Richard R. Forberg, Nov 16 2014
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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) = 8a(n-1)-8a(n-2)+a(n-3).
G.f.: -5*(x^2-4*x+1)/((x-1)*(x^2-7*x+1)). - Colin Barker, Jun 25 2012
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MAPLE
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luc := proc(n) 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 40 do printf(`%d, `, luc(4*n+2)+2) od: # James A. Sellers, Mar 05 2003
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MATHEMATICA
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Table[LucasL[4n+2]+2, {n, 0, 20}] (* or *)
Table[5Fibonacci[2n+1]^2, {n, 0, 30}] (* Harvey P. Dale, Apr 18 2011 *)
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PROG
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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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