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 A087281 a(n) = Lucas(7*n). 10
 2, 29, 843, 24476, 710647, 20633239, 599074578, 17393796001, 505019158607, 14662949395604, 425730551631123, 12360848946698171, 358890350005878082, 10420180999117162549, 302544139324403592003, 8784200221406821330636, 255044350560122222180447, 7405070366464951264563599 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS a(n+1)/a(n) converges to (29+sqrt(845))/2 = 29.0344418537... a(0)/a(1) = 2/29, a(1)/a(2) = 29/843, a(2)/a(3) = 843/24476, a(3)/a(4) = 24476/710647, etc. Lim_{n->infinity} a(n)/a(n+1) = 0.0344418537... = 2/(29+sqrt(845)) = (sqrt(845)-29)/2. LINKS Table of n, a(n) for n=0..17. Tanya Khovanova, Recursive Sequences Index entries for recurrences a(n) = k*a(n - 1) +/- a(n - 2) Index entries for linear recurrences with constant coefficients, signature (29, 1). FORMULA a(n) = 29*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 29. a(n) = ((29 + sqrt(845))/2)^n + ((29 - sqrt(845))/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.: (2-29*x)/(1-29*x-x^2). - Philippe Deléham, Nov 02 2008 EXAMPLE a(4) = 710647 = 29*a(3) + a(2) = 29*24476 + 843 = ((29+sqrt(845))/2)^4 + ((29-sqrt(845))/2)^4 = 710646.9999985928... + 0.0000014071... = 710647. MATHEMATICA LucasL[7Range[0, 20]] (* or *) LinearRecurrence[{29, 1}, {2, 29}, 20] (* Harvey P. Dale, Nov 22 2011 *) PROG (Magma) [ Lucas(7*n) : n in [0..100]]; // Vincenzo Librandi, Apr 14 2011 CROSSREFS Cf. A000032. Sequence in context: A282735 A245252 A090251 * A024234 A367551 A077282 Adjacent sequences: A087278 A087279 A087280 * A087282 A087283 A087284 KEYWORD easy,nonn AUTHOR Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Oct 19 2003 EXTENSIONS More terms from Ray Chandler, Feb 14 2004 More terms from Vincenzo Librandi, Apr 14 2011 STATUS approved

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Last modified July 23 16:21 EDT 2024. Contains 374552 sequences. (Running on oeis4.)