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 A081070 Lucas(4n)-2, or 5*Fibonacci(2n)^2. 3
 0, 5, 45, 320, 2205, 15125, 103680, 710645, 4870845, 33385280, 228826125, 1568397605, 10749957120, 73681302245, 505019158605, 3461452808000, 23725150497405, 162614600673845, 1114577054219520, 7639424778862805 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 REFERENCES Hugh C. Williams, Edouard Lucas and Primality Testing, John Wiley and Sons, 1998, p. 75. LINKS Hang Gu and Robert M. Ziff, Crossing on hyperbolic lattices, arXiv:1111.5626 [cond-mat.dis-nn], 2011-2012 (see Eq. 4). Index entries for linear recurrences with constant coefficients, signature (8,-8,1). FORMULA a(n) = 8*a(n-1) - 8*a(n-2) + a(n-3). a(n) = 5*A049684(n). a(n) = -2+[(7/2)-(3/2)*sqrt(5)]^n+[(7/2)+(3/2)*sqrt(5)]^n, with n>=0. - Paolo P. Lava, Dec 01 2008 G.f.: 5*x*(x+1)/((1-x)*(x^2-7*x+1)). - Colin Barker, Jun 24 2012 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) od: # James A. Sellers, Mar 05 2003 MATHEMATICA LinearRecurrence[{8, -8, 1}, {0, 5, 45}, 20] (* Jean-François Alcover, Nov 24 2017 *) PROG (MAGMA) [Lucas(4*n)-2: n in [0..30]]; // Vincenzo Librandi, Apr 21 2011 (PARI) a(n) = 5*fibonacci(2*n)^2; \\ Michel Marcus, Nov 24 2017 CROSSREFS Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers), A049684. Sequence in context: A249638 A188349 A241275 * A247494 A043025 A190540 Adjacent sequences:  A081067 A081068 A081069 * A081071 A081072 A081073 KEYWORD nonn,easy AUTHOR R. K. Guy, Mar 04 2003 STATUS approved

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Last modified February 18 02:09 EST 2018. Contains 299297 sequences. (Running on oeis4.)