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 A087619 a(n) = 137a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 137. 0
 2, 137, 18771, 2571764, 352350439, 48274581907, 6613970071698, 906162174404533, 124150831863492719, 17009570127472907036, 2330435258295651756651, 319286639956631763568223 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS a(n+1)/a(n) converges to (137+sqrt(18773))/2 = 137.00729888121410965... a(0)/a(1) = 2/137; a(1)/a(2) = 137/18771; a(2)/a(3) = 18771/2571764; a(3)/a(4) = 2571764/352350439; ... etc. Lim a(n)/a(n+1) as n approaches infinity = 0.00729888121410965... = 2/(137+sqrt(18773)) = (sqrt(18773)-137)/2. LINKS Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (137, 1). FORMULA a(n) =137a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 137, a(n) = ((137+sqrt(18773))/2)^n + ((137-sqrt(18773))/2)^n, (a(n))^2 =a(2n)-2 if n=1, 3, 5..., (a(n))^2 =a(2n)+2 if n=2, 4, 6.... G.f.: (2-137*x)/(1-137*x-x^2). [From Philippe Deléham, Nov 23 2008] EXAMPLE a(4) = 352350439 = 137a(3) + a(2) = 137*2571764+ 18771 = ((137+sqrt(18773))/2)^4 + ( (137-sqrt(18773))/2)^4 = 352350438.999999997161916 + 0.000000002838083 = 352350439. CROSSREFS Cf. A037088, A073481. Sequence in context: A139907 A195379 A221227 * A157072 A051029 A212715 Adjacent sequences:  A087616 A087617 A087618 * A087620 A087621 A087622 KEYWORD easy,nonn AUTHOR Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Oct 25 2003 STATUS approved

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