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 A089775 Lucas numbers L(12n). 3
 2, 322, 103682, 33385282, 10749957122, 3461452808002, 1114577054219522, 358890350005878082, 115561578124838522882, 37210469265847998489922, 11981655542024930675232002, 3858055874062761829426214722, 1242282009792667284144565908482, 400010949097364802732720796316482 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS a(n+1)/a(n) converges to (322 + sqrt(103680))/2 = 321.996894379... a(0)/a(1) = 2/322; a(1)/a(2) = 322/103682; a(2)/a(3) = 103682/33385282; a(3)/a(4) = 33385282/10749957122; etc. Lim_{n -> inf} a(n)/a(n+1) = 0.00310562... = 2/(322 + sqrt(103680)) = (322 - sqrt(103680))/2. LINKS Nathaniel Johnston, Table of n, a(n) for n = 0..100 Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (322, -1). FORMULA a(n) = 322*a(n-1) - a(n-2), starting with a(0) = 2 and a(1) = 322 a(n) = ((322 + sqrt(103680))/2)^n + ((322 - sqrt(103680))/2)^n. (a(n))^2 = a(2n) + 2. G.f.: (2-322*x)/(1-322*x+x^2). - Philippe Deléham, Nov 02 2008 EXAMPLE a(4) = 10749957122 = 322*a(3) - a(2) = 322*33385282 - 103682 = ((322 + sqrt(103680))/2)^4 + ((322 - sqrt(103680))/2)^4. MATHEMATICA Table[LucasL[12n], {n, 0, 13}] (* Indranil Ghosh, Mar 15 2017 *) PROG (MAGMA) [ Lucas(12*n) : n in [0..70]]; // Vincenzo Librandi, Apr 15 2011 (PARI) Vec((2 - 322*x)/(1 - 322*x + x^2) + O(x^14)) \\ Indranil Ghosh, Mar 15 2017 CROSSREFS Cf. A000032, A060964. a(n) = A000032(12n). Row 9 * 2 of array A188644 Sequence in context: A118579 A221190 A192725 * A094402 A262637 A028483 Adjacent sequences:  A089772 A089773 A089774 * A089776 A089777 A089778 KEYWORD easy,nonn AUTHOR Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Jan 09 2004 EXTENSIONS a(11) - a(13) from Vincenzo Librandi, Apr 15 2011 STATUS approved

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Last modified December 12 16:06 EST 2018. Contains 318077 sequences. (Running on oeis4.)