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A145331 Numbers X such that there exists Y in N : X^2=129*Y^2+43. 1
602, 20292818, 684070894178, 23060029822447562, 777353604630636420842, 26204589989038723924136258, 883356727753141778851996836338, 29777955266353819376062089428817722, 1003814871145430523413911255793448572282 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..200

Index entries for linear recurrences with constant coefficients, signature (33710,-1).

FORMULA

a(n+2) = 33710*a(n+1)-a(n).

a(n) = 301*{[16855+1484*sqrt(129)]^n+[16855-1484*sqrt(129)]^n}-(53/2)*sqrt(129)*{[16855-1484*sqrt(129)]^n-[16855 +1484*sqrt(129)]^n} with n>=0. - Paolo P. Lava, Nov 25 2008

G.f.: -602*x*(x-1) / (x^2-33710*x+1). - Colin Barker, Oct 21 2014

EXAMPLE

a(1)=602 because the first relation is 602^2=129*53^2+43.

MATHEMATICA

CoefficientList[Series[602(1 - x)/(x^2 - 33710 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 21 2014 *)

PROG

(PARI) Vec(-602*x*(x-1)/(x^2-33710*x+1) + O(x^20)) \\ Colin Barker, Oct 21 2014

(MAGMA) I:=[602, 20292818]; [n le 2 select I[n] else 33710*Self(n-1)-Self(n-2): n in [1..10]]; // Vincenzo Librandi Oct 21 2014

CROSSREFS

Sequence in context: A218650 A218180 A218521 * A252957 A348077 A066785

Adjacent sequences:  A145328 A145329 A145330 * A145332 A145333 A145334

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Oct 08 2008

EXTENSIONS

Editing from Colin Barker, Oct 21 2014

STATUS

approved

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Last modified October 22 18:45 EDT 2021. Contains 348175 sequences. (Running on oeis4.)