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 A090306 a(n) = 17a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 17. 5
 2, 17, 291, 4964, 84679, 1444507, 24641298, 420346573, 7170533039, 122319408236, 2086600473051, 35594527450103, 607193567124802, 10357885168571737, 176691241432844331, 3014108989526925364, 51416544063390575519 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 COMMENTS a(n+1)/a(n) converges to (17+sqrt(293))/2 = 17.058621... Lim a(n)/a(n+1) as n approaches infinity = 0.058621... = 2/(17+sqrt(293)) = (sqrt(293)-17)/2. Lim a(n+1)/a(n) as n approaches infinity = 17.058621... = (17+sqrt(293))/2 = 2/(sqrt(293)-17). 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 (17, 1). FORMULA a(n) =17a(n-1) + a(n-2), starting with a(0) = 2 and a(1) = 17. a(n) = ((17+sqrt(293))/2)^n + ((17-sqrt(293))/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.: (2-17x)/(1-17x-x^2). [From Philippe Deléham, Nov 02 2008] Contribution from Johannes W. Meijer, Jun 12 2010: (Start) a(2n+1) = 17*A098249(n). a(3n+1) = A041550(5n), a(3n+2) = A041550(5n+3), a(3n+3) = 2*A041550(5n+4). Limit(a(n+k)/a(k), k=infinity) = (A090306(n) + A178765(n)*sqrt(293))/2 Limit(A090306(n)/A178765(n), n=infinity) = sqrt(293) (End) EXAMPLE a(4) = 84679 = 17a(3) + a(2) = 17*4964+ 291=((17+sqrt(293))/2)^4 + ((17-sqrt(293))/2)^4 = 84678.999988190 + 0.000011809 =84679. MATHEMATICA LinearRecurrence[{17, 1}, {2, 17}, 30] (* Harvey P. Dale, Jan 24 2018 *) CROSSREFS Cf. A005074. Sequence in context: A198287 A268705 A078367 * A304857 A007785 A201785 Adjacent sequences:  A090303 A090304 A090305 * A090307 A090308 A090309 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 October 20 10:00 EDT 2019. Contains 328257 sequences. (Running on oeis4.)