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 A090301 a(n) = 15a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 15. 5
 2, 15, 227, 3420, 51527, 776325, 11696402, 176222355, 2655031727, 40001698260, 602680505627, 9080209282665, 136805819745602, 2061167505466695, 31054318401746027, 467875943531657100, 7049193471376602527 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS a(n+1)/a(n) converges to (15+sqrt(229))/2 = 15.066372... Lim a(n)/a(n+1) as n approaches infinity = 0.066372... = 2/(15+sqrt(229)) = (sqrt(229)-15)/2. Lim a(n+1)/a(n) as n approaches infinity = 15.066372... = (15+sqrt(229))/2 = 2/(sqrt(229)-15). Contribution from Johannes W. Meijer, Jun 12 2010: (Start) For more information about this type of recurrence follow the Khovanova link and see A054413, A086902 and A178765. (End) LINKS Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (15, 1). FORMULA a(n) =15a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 15. a(n) = ((15+sqrt(229))/2)^n + ((15-sqrt(229))/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.: (2-15*x)/(1-15*x-x^2). [From Philippe Deléham, Nov 02 2008] Contribution from Johannes W. Meijer, Jun 12 2010: (Start) Limit(a(n+k)/a(k), k=infinity) = (A090301(n) + A154597(n)*sqrt(229))/2 Limit(A090301(n)/ A154597(n), n=infinity) = sqrt(229) (End) EXAMPLE a(4) = 51527 = 15a(3) + a(2) = 15*3420+ 227=((15+sqrt(229))/2)^4 + ((15-sqrt(229))/2)^4 = 51526.9999805 + 0.0000194 =51527 CROSSREFS Cf. A058087, A071416. Contribution from Johannes W. Meijer, Jun 12 2010: (Start) a(2n+1) = 15*A098246(n). a(3n+1) = A041426(5n), a(3n+2) = A041426(5n+3), a(3n+3) = 2*A041426(5n+4). (End) Sequence in context: A176337 A145168 A184357 * A297087 A247660 A197236 Adjacent sequences:  A090298 A090299 A090300 * A090302 A090303 A090304 KEYWORD easy,nonn AUTHOR Nikolay V. Kosinov (kosinov(AT)unitron.com.ua), Jan 25 2004 EXTENSIONS More terms from Ray Chandler, Feb 14 2004 STATUS approved

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Last modified January 16 11:42 EST 2019. Contains 319188 sequences. (Running on oeis4.)