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 A201157 y-values in the solution to 5*x^2 - 20 = y^2. 3
 0, 5, 15, 40, 105, 275, 720, 1885, 4935, 12920, 33825, 88555, 231840, 606965, 1589055, 4160200, 10891545, 28514435, 74651760, 195440845, 511670775, 1339571480, 3507043665, 9181559515, 24037634880, 62931345125, 164756400495, 431337856360, 1129257168585 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS Except a(1), the same as A054888. - R. J. Mathar, Nov 28 2011 LINKS Michael De Vlieger, Table of n, a(n) for n = 1..2392 Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, Ellipse Chains and Associated Sequences, J. Int. Seq., Vol. 23 (2020), Article 20.8.5. Index entries for linear recurrences with constant coefficients, signature (3,-1). FORMULA a(n) = 3*a(n-1) - a(n-2), n>2. G.f.: 5*x^2 / (x^2 - 3*x + 1). - Colin Barker, Apr 08 2013 a(n) = 5*Fibonacci(2*n-2) = Lucas(2*n-1) + Lucas(2*n-3) with Lucas(-1) = -1. - Bruno Berselli, Feb 15 2017 a(n) = Lucas(n)^2 - Lucas(n-2)^2. - Greg Dresden, Apr 15 2022 EXAMPLE 15 is in the sequence because 15^2 = 5*7^2 - 20. MATHEMATICA LinearRecurrence[{3, -1}, {0, 5}, 50] CROSSREFS Cf. A000032, A005248. Sequence in context: A000333 A291225 A054888 * A301980 A230955 A038066 Adjacent sequences:  A201154 A201155 A201156 * A201158 A201159 A201160 KEYWORD nonn,easy AUTHOR Sture Sjöstedt, Nov 27 2011 EXTENSIONS More terms from Colin Barker, Apr 08 2013 STATUS approved

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Last modified July 7 02:44 EDT 2022. Contains 355141 sequences. (Running on oeis4.)