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 A081077 a(n) = Lucas(4*n+2) + 3, or Lucas(2*n)*Lucas(2*n+2). 0
 6, 21, 126, 846, 5781, 39606, 271446, 1860501, 12752046, 87403806, 599074581, 4106118246, 28143753126, 192900153621, 1322157322206, 9062201101806, 62113250390421, 425730551631126, 2918000611027446, 20000273725560981 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 REFERENCES Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75. LINKS Index entries for linear recurrences with constant coefficients, signature (8,-8,1). FORMULA 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 MAPLE 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 MATHEMATICA Table[LucasL[4*n + 2] + 3, {n, 0, 30}] (* Amiram Eldar, Oct 05 2020 *) PROG (PARI) Vec(-3*(2-9*x+2*x^2)/(x-1)/(x^2-7*x+1) + O(x^30)) \\ Michel Marcus, Dec 23 2014 CROSSREFS Cf. A000032 (Lucas numbers), A081067. Sequence in context: A012840 A013320 A056308 * A093775 A318103 A058821 Adjacent sequences:  A081074 A081075 A081076 * A081078 A081079 A081080 KEYWORD nonn,easy AUTHOR R. K. Guy, Mar 04 2003 EXTENSIONS More terms from James A. Sellers, Mar 05 2003 STATUS approved

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Last modified May 25 03:36 EDT 2022. Contains 354047 sequences. (Running on oeis4.)