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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.)