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A145526 Numbers Y such that 273*Y^2+91 is a square. 1
11, 16005, 23271259, 33836394581, 49198094449515, 71533995493200229, 104010380249018683451, 151231021348077672537525, 219889801029724686850877899, 319719619466198346603503927621, 464872106814051366236807859883035 (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 (1454,-1).

FORMULA

a(n+2) = 1454*a(n+1)-a(n).

a(n) = (11/2)*{[727-44*sqrt(273)]^n+[727+44*sqrt(273)]^n}-(1/3)*sqrt(273)*{[727-44*sqrt(273)]^n -[727+44*sqrt(273)]^n} with n>=0. - Paolo P. Lava, Nov 25 2008

G.f.: 11*x*(x+1) / (x^2-1454*x+1). - Colin Barker, Oct 21 2014

EXAMPLE

a(1)=11 because the first relation is : 182^2=273*11^2+91.

MATHEMATICA

CoefficientList[Series[11 (x + 1)/(x^2 - 1454 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 21 2014 *)

PROG

(PARI) Vec(11*x*(x+1)/(x^2-1454*x+1) + O(x^20)) \\ Colin Barker, Oct 21 2014

(MAGMA) I:=[11, 16005]; [n le 2 select I[n] else 1454*Self(n-1)-Self(n-2): n in [1..15]]; // Vincenzo Librandi, Oct 21 2014

CROSSREFS

Sequence in context: A013748 A076783 A249645 * A230220 A068647 A199148

Adjacent sequences:  A145523 A145524 A145525 * A145527 A145528 A145529

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Oct 12 2008

EXTENSIONS

Editing from Colin Barker, Oct 21 2014

STATUS

approved

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Last modified June 21 06:05 EDT 2021. Contains 345356 sequences. (Running on oeis4.)