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A145693 Numbers X such that there exists Y in N with X^2=21*Y^2+7. 1
14, 1526, 167846, 18461534, 2030600894, 223347636806, 24566209447766, 2702059691617454, 297201999868472174, 32689517925840321686, 3595549769842566913286, 395477785164756520139774, 43498960818353374648461854, 4784490212233706454810664166 (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 (110,-1).

FORMULA

a(n+2) = 110*a(n+1)-a(n).

a(n) = 7*{[55+12*sqrt(21)]^n+[55-12*sqrt(21)]^n}+(3/2)*sqrt(21)*{[55+12*sqrt(21)]^n-[55-12*sqrt(21)]^n} with n>=0. - Paolo P. Lava, Nov 25 2008

G.f.: -14*x*(x-1) / (x^2-110*x+1). - Colin Barker, Oct 21 2014

EXAMPLE

a(1)=14 because the first relation is 14^2=21*3^2+7.

MATHEMATICA

CoefficientList[Series[14 (1 - x)/(x^2 - 110 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 21 2014 *)

PROG

(PARI) Vec(-14*x*(x-1)/(x^2-110*x+1) + O(x^20)) \\ Colin Barker, Oct 21 2014

(MAGMA) I:=[14, 1526]; [n le 2 select I[n] else 110*Self(n-1)-Self(n-2): n in [1..15]]; // Vincenzo Librandi, Oct 21 2014

CROSSREFS

Cf. A144927, A144928, A144929, A144930.

Sequence in context: A131582 A270858 A160246 * A279326 A200459 A164524

Adjacent sequences:  A145690 A145691 A145692 * A145694 A145695 A145696

KEYWORD

easy,nonn

AUTHOR

Richard Choulet, Oct 16 2008

EXTENSIONS

Editing and more terms from Colin Barker, Oct 21 2014

STATUS

approved

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Last modified October 19 11:49 EDT 2021. Contains 348088 sequences. (Running on oeis4.)