A201157 y-values in the solution to 5*x^2 - 20 = y^2.
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
Offset: 1
Examples
15 is in the sequence because 15^2 = 5*7^2 - 20.
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).
Programs
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Mathematica
LinearRecurrence[{3, -1}, {0, 5}, 50]
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
Extensions
More terms from Colin Barker, Apr 08 2013
Comments