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%I #30 Apr 15 2022 23:40:02
%S 0,5,15,40,105,275,720,1885,4935,12920,33825,88555,231840,606965,
%T 1589055,4160200,10891545,28514435,74651760,195440845,511670775,
%U 1339571480,3507043665,9181559515,24037634880,62931345125,164756400495,431337856360,1129257168585
%N y-values in the solution to 5*x^2 - 20 = y^2.
%C Except a(1), the same as A054888. - _R. J. Mathar_, Nov 28 2011
%H Michael De Vlieger, <a href="/A201157/b201157.txt">Table of n, a(n) for n = 1..2392</a>
%H Hacène Belbachir, Soumeya Merwa Tebtoub, and László Németh, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL23/Nemeth/nemeth7.html">Ellipse Chains and Associated Sequences</a>, J. Int. Seq., Vol. 23 (2020), Article 20.8.5.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1).
%F a(n) = 3*a(n-1) - a(n-2), n>2.
%F G.f.: 5*x^2 / (x^2 - 3*x + 1). - _Colin Barker_, Apr 08 2013
%F a(n) = 5*Fibonacci(2*n-2) = Lucas(2*n-1) + Lucas(2*n-3) with Lucas(-1) = -1. - _Bruno Berselli_, Feb 15 2017
%F a(n) = Lucas(n)^2 - Lucas(n-2)^2. - _Greg Dresden_, Apr 15 2022
%e 15 is in the sequence because 15^2 = 5*7^2 - 20.
%t LinearRecurrence[{3, -1}, {0, 5}, 50]
%Y Cf. A000032, A005248.
%K nonn,easy
%O 1,2
%A _Sture Sjöstedt_, Nov 27 2011
%E More terms from _Colin Barker_, Apr 08 2013
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