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A131216 Numbers X such that 99*X^2 - 2178 is a square. 2
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

G. C. Greubel, Table of n, a(n) for n = 1..750

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*(1-z)/(1-20*z+z^2) - Richard Choulet, Oct 09 2007

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

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

MAPLE

seq(coeff(series(11*x*(1-x)/(1-20*x+x^2), x, n+1), x, n), n = 0..20); # G. C. Greubel, Dec 06 2019

MATHEMATICA

LinearRecurrence[{20, -1}, {11, 209}, 20] (* G. C. Greubel, Dec 06 2019 *)

PROG

(PARI) my(x='x+O('x^20)); Vec(11*x*(1-x)/(1-20*x+x^2)) \\ G. C. Greubel, Dec 06 2019

(MAGMA) R<x>:=PowerSeriesRing(Integers(), 20); Coefficients(R!( 11*x*(1-x)/(1-20*x+x^2) )); // G. C. Greubel, Dec 06 2019

(Sage)

def A131216_list(prec):

    P.<x> = PowerSeriesRing(ZZ, prec)

    return P( 11*x*(1-x)/(1-20*x+x^2) ).list()

A131216_list(20) # G. C. Greubel, Dec 06 2019

(GAP) a:=[11, 209];; for n in [3..20] do a[n]:=20*a[n-1]-a[n-2]; od; a; # G. C. Greubel, Dec 06 2019

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 September 24 22:46 EDT 2021. Contains 347651 sequences. (Running on oeis4.)