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A131216 Numbers X such that 99*X^2-2178 is a square. 1
11, 209, 4169, 83171, 1659251, 33101849, 660377729, 13174452731, 262828676891, 5243399085089, 104605153024889, 2086859661412691, 41632588075228931, 830564901843165929, 16569665448788089649, 330562744073918627051 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Table of n, a(n) for n=1..16.

Index entries for linear recurrences with constant coefficients, signature (20,-1).

FORMULA

a(n+2)=20*a(n+1)-a(n).

a(n+1)=10*a(n+1)+ sqrt(99*a(n)^2-2178).

G.f.: (11*z-11*z^2)/(1-20*z+z^2) - Richard Choulet, Oct 09 2007

a(n)=(3/2)*[10+3*sqrt(11)]^(n-1)*sqrt(11)+(11/2)*[10+3*sqrt(11)]^(n-1)-(3/2)*sqrt(11)*[10-3 *sqrt(11)]^(n-1)+(11/2)*[10-3*sqrt(11)]^(n-1), with n>=1 - Paolo P. Lava, Jul 15 2008

a(n) = 11*A075839(n-1). - R. J. Mathar, Aug 22 2012

CROSSREFS

Cf. A083043.

Sequence in context: A020518 A196849 A196699 * A034909 A081788 A060496

Adjacent sequences:  A131213 A131214 A131215 * A131217 A131218 A131219

KEYWORD

nonn,easy

AUTHOR

Richard Choulet, Sep 27 2007

STATUS

approved

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Last modified May 19 14:36 EDT 2019. Contains 323395 sequences. (Running on oeis4.)