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A201157
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y-values in the solution to 5*x^2 - 20 = y^2.
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3
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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
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OFFSET
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1,2
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COMMENTS
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Except a(1), the same as A054888. - R. J. Mathar, Nov 28 2011
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LINKS
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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).
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FORMULA
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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
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EXAMPLE
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15 is in the sequence because 15^2 = 5*7^2 - 20.
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MATHEMATICA
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LinearRecurrence[{3, -1}, {0, 5}, 50]
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CROSSREFS
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Cf. A000032, A005248.
Sequence in context: A000333 A291225 A054888 * A301980 A230955 A038066
Adjacent sequences: A201154 A201155 A201156 * A201158 A201159 A201160
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KEYWORD
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nonn,easy
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AUTHOR
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Sture Sjöstedt, Nov 27 2011
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EXTENSIONS
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More terms from Colin Barker, Apr 08 2013
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STATUS
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approved
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