

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
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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+[5512*sqrt(21)]^n}+(3/2)*sqrt(21)*{[55+12*sqrt(21)]^n[5512*sqrt(21)]^n} with n>=0.  Paolo P. Lava, Nov 25 2008
G.f.: 14*x*(x1) / (x^2110*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*(x1)/(x^2110*x+1) + O(x^20)) \\ Colin Barker, Oct 21 2014
(MAGMA) I:=[14, 1526]; [n le 2 select I[n] else 110*Self(n1)Self(n2): 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



