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 A081015 a(n) = Lucas(4n+3) + 1, or 5*Fibonacci(2n+1)*Fibonacci(2n+2). 3
 5, 30, 200, 1365, 9350, 64080, 439205, 3010350, 20633240, 141422325, 969323030, 6643838880, 45537549125, 312119004990, 2139295485800, 14662949395605, 100501350283430, 688846502588400, 4721424167835365, 32361122672259150, 221806434537978680, 1520283919093591605 (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 G. C. Greubel, Table of n, a(n) for n = 0..1000 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) = 1+2*{[(7/2)-(3/2)*sqrt(5)]^n+[(7/2)+(3/2)*sqrt(5)]^n}+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 G.f.: 5*(1-2*x)/((1-x)*(1-7*x+x^2)). - 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 25 do printf(`%d, `, luc(4*n+3)+1) od: # James A. Sellers, Mar 03 2003 MATHEMATICA LucasL[4*Range[0, 20] +3] +1 (* G. C. Greubel, Jul 14 2019 *) LinearRecurrence[{8, -8, 1}, {5, 30, 200}, 30] (* Harvey P. Dale, Dec 06 2021 *) PROG (PARI) vector(30, n, n--; f=fibonacci; f(4*n+4)+f(4*n+2)+1) \\ G. C. Greubel, Jul 14 2019 (Magma) [Lucas(4*n+3)+1: n in [0..30]]; // G. C. Greubel, Jul 14 2019 (Sage) [lucas_number2(4*n+3, 1, -1)+1 for n in (0..30)] # G. C. Greubel, Jul 14 2019 (GAP) List([0..30], n-> Lucas(1, -1, 4*n+3)[2] +1); # G. C. Greubel, Jul 14 2019 (Python) from sympy import lucas def a(n): return lucas(4*n+3) + 1 print([a(n) for n in range(22)]) # Michael S. Branicky, May 30 2021 CROSSREFS Cf. A000045 (Fibonacci numbers), A000032 (Lucas numbers). Sequence in context: A034164 A322257 A103433 * A090139 A107265 A196678 Adjacent sequences: A081012 A081013 A081014 * A081016 A081017 A081018 KEYWORD nonn,easy AUTHOR R. K. Guy, Mar 01 2003 EXTENSIONS More terms from James A. Sellers, Mar 03 2003 STATUS approved

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Last modified January 30 12:56 EST 2023. Contains 359945 sequences. (Running on oeis4.)