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 A087287 a(n) = Lucas(9*n). 2
 2, 76, 5778, 439204, 33385282, 2537720636, 192900153618, 14662949395604, 1114577054219522, 84722519070079276, 6440026026380244498, 489526700523968661124, 37210469265847998489922, 2828485190904971853895196, 215002084978043708894524818, 16342986943522226847837781364, 1242282009792667284144565908482 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS a(n+1)/a(n) converges to (76 + sqrt(5780))/2 = 76.01315561749... a(0)/a(1) = 2/76, a(1)/a(2) = 76/5778, a(2)/a(3) = 5778/439204, a(3)/a(4) = 439204/33385282, etc. Lim_{n->infinity} a(n)/a(n+1) = 0.01315561749... = 2/(76 + sqrt(5780)) = (sqrt(5780) - 76)/2. LINKS Indranil Ghosh, Table of n, a(n) for n = 0..530 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (76, 1). FORMULA a(n) = 76a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 76. a(n) = ((76 + sqrt(5780))/2)^n + ((76 - sqrt(5780))/2)^n. a(n)^2 = a(2n) - 2 for n = 1, 3, 5, ...; a(n)^2 = a(2n) + 2 for n = 2, 4, 6, .... G.f.: (2-76*x)/(1-76*x-x^2). - Philippe Deléham, Nov 02 2008 EXAMPLE a(4) = 33385282 = 76*a(3) + a(2) = 76*439204 + 5778 = ((76 + sqrt(5780))/2)^4 + ((76 - sqrt(5780))/2)^4 = 33385281.999999970046... + 0.000000029953... = 33385282. PROG (MAGMA) [ Lucas(9*n) : n in [0..100]]; // Vincenzo Librandi, Apr 14 2011 (PARI) a(n)=fibonacci(9*n-1)+fibonacci(9*n+1) \\ Charles R Greathouse IV, Feb 06 2017 CROSSREFS Cf. A000032. Sequence in context: A198651 A198658 A277298 * A266877 A301472 A041721 Adjacent sequences:  A087284 A087285 A087286 * A087288 A087289 A087290 KEYWORD easy,nonn AUTHOR Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Oct 19 2003 EXTENSIONS More terms from Vincenzo Librandi, Apr 14 2011 STATUS approved

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Last modified November 16 23:51 EST 2018. Contains 317275 sequences. (Running on oeis4.)