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 A088316 a(n) = 13*a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 13. 5
 2, 13, 171, 2236, 29239, 382343, 4999698, 65378417, 854919119, 11179326964, 146186169651, 1911599532427, 24996980091202, 326872340718053, 4274337409425891, 55893258663254636, 730886700031736159 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS a(n+1)/a(n) converges to (13+sqrt(173))/2. Lim a(n)/a(n+1) as n approaches infinity = 0.07647321... = 2/(13+sqrt(173)). For more information about this type of recurrence follow the Khovanova link and see A086902 and A054413. - Johannes W. Meijer, Jun 12 2010 LINKS Tanya Khovanova, Recursive Sequences Index entries for linear recurrences with constant coefficients, signature (13, 1). FORMULA a(n) = ((13+sqrt(173))/2)^n + ((13-sqrt(173))/2)^n. G.f.: (2-13*x)/(1-13*x-x^2). [Philippe Deléham, Nov 02 2008] From Johannes W. Meijer, Jun 12 2010: (Start) a(2*n+1) = 13*A097845(n). a(3*n+1) = A041318(5n), a(3n+2) = A041318(5n+3), a(3n+3) = 2*A041318(5n+4). Limit(a(n+k)/a(k), k=infinity) = (A088316(n) + A140455(n)*sqrt(173))/2. Limit(A088316(n)/A140455(n), n=infinity) = sqrt(173). (End) EXAMPLE a(4) = 29239 = 13a(3) + a(2) = 13*2236 + 171 = ((13+sqrt(173))/2)^4 + ((13-sqrt(173))/2)^4 = 29239. CROSSREFS Cf. A006905. Sequence in context: A258224 A078363 A143851 * A006905 A119400 A182314 Adjacent sequences:  A088313 A088314 A088315 * A088317 A088318 A088319 KEYWORD nonn,easy AUTHOR Nikolay V. Kosinov, Dmitry V. Polyakov (kosinov(AT)unitron.com.ua), Nov 06 2003 STATUS approved

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Last modified August 17 17:02 EDT 2018. Contains 313816 sequences. (Running on oeis4.)