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A145715 Numbers X such that there exists Y in N with X^2 = 381*Y^2 + 127. 1
254, 515366, 1046192726, 2123770718414, 4311253512187694, 8751842505970300406, 17766235975866197636486, 36065450279165875231766174, 73212846300470750854287696734, 148622041924505345068328792603846 (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 (2030,-1).

FORMULA

a(n+2) = 2030*a(n+1) - a(n).

a(n) = 127*((1015+52*sqrt(381))^n + (1015-52*sqrt(381))^n) + (13/2)*sqrt(381)*((1015+52*sqrt(381))^n - (1015-52*sqrt(381))^n) with n>=0. - Paolo P. Lava, Nov 25 2008

G.f.: -254*x*(x-1) / (x^2-2030*x+1). - Colin Barker, Oct 21 2014

EXAMPLE

a(1)=254 because the first relation is 254^2=381*13^2+127.

MATHEMATICA

LinearRecurrence[{2030, -1}, {254, 515366}, 10] (* Harvey P. Dale, Dec 21 2011 *)

CoefficientList[Series[254 (1 - x)/(x^2 - 2030 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 21 2014 *)

PROG

(PARI) Vec(-254*x*(x-1)/(x^2-2030*x+1) + O(x^20)) \\ Colin Barker, Oct 21 2014

(MAGMA) I:=[254, 515366]; [n le 2 select I[n] else 2030*Self(n-1)-Self(n-2): n in [1..15]]; // Vincenzo Librandi, Oct 21 2014

CROSSREFS

Sequence in context: A250566 A278155 A251860 * A145587 A283188 A028526

Adjacent sequences:  A145712 A145713 A145714 * A145716 A145717 A145718

KEYWORD

nonn,easy

AUTHOR

Richard Choulet, Oct 16 2008

EXTENSIONS

Edited by Colin Barker, Oct 21 2014

STATUS

approved

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Last modified January 29 04:57 EST 2020. Contains 331335 sequences. (Running on oeis4.)