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A081077
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a(n) = Lucas(4*n+2) + 3, or Lucas(2*n)*Lucas(2*n+2).
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0
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6, 21, 126, 846, 5781, 39606, 271446, 1860501, 12752046, 87403806, 599074581, 4106118246, 28143753126, 192900153621, 1322157322206, 9062201101806, 62113250390421, 425730551631126, 2918000611027446, 20000273725560981
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OFFSET
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0,1
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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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Table of n, a(n) for n=0..19.
Index entries for linear recurrences with constant coefficients, signature (8,-8,1).
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FORMULA
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a(n) = 8a(n-1) - 8a(n-2) + a(n-3).
a(n) = A081067(n)+1. - R. J. Mathar, May 18 2007
G.f.: -3*(2-9*x+2*x^2)/(x-1)/(x^2-7*x+1) = -3/(x-1)+(-3*x+3)/(x^2-7*x+1). - R. J. Mathar, Nov 18 2007
a(n) = 3+(3/2)*{[(7/2)-(3/2)*sqrt(5)]^n+[(7/2)+(3/2)*sqrt(5)]^n}+(1/2)*sqrt(5)*{[(7/2)+(3/2) *sqrt(5)]^n-[(7/2)-(3/2)*sqrt(5)]^n}, with n>=0. - Paolo P. Lava, Dec 01 2008
Sum_{n>=0} 1/a(n) = sqrt(5)/10. - Amiram Eldar, Oct 05 2020
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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)+3) od: # James A. Sellers, Mar 05 2003
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MATHEMATICA
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Table[LucasL[4*n + 2] + 3, {n, 0, 30}] (* Amiram Eldar, Oct 05 2020 *)
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PROG
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(PARI) Vec(-3*(2-9*x+2*x^2)/(x-1)/(x^2-7*x+1) + O(x^30)) \\ Michel Marcus, Dec 23 2014
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CROSSREFS
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Cf. A000032 (Lucas numbers), A081067.
Sequence in context: A012840 A013320 A056308 * A093775 A318103 A058821
Adjacent sequences: A081074 A081075 A081076 * A081078 A081079 A081080
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KEYWORD
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nonn,easy
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AUTHOR
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R. K. Guy, Mar 04 2003
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EXTENSIONS
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More terms from James A. Sellers, Mar 05 2003
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STATUS
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approved
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