A145693 Numbers X such that there exists Y in N with X^2=21*Y^2+7.
14, 1526, 167846, 18461534, 2030600894, 223347636806, 24566209447766, 2702059691617454, 297201999868472174, 32689517925840321686, 3595549769842566913286, 395477785164756520139774, 43498960818353374648461854, 4784490212233706454810664166
Offset: 1
Examples
a(1)=14 because the first relation is 14^2=21*3^2+7.
Links
- Vincenzo Librandi, Table of n, a(n) for n = 1..200
- Index entries for linear recurrences with constant coefficients, signature (110,-1).
Programs
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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
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Mathematica
CoefficientList[Series[14 (1 - x)/(x^2 - 110 x + 1), {x, 0, 20}], x] (* Vincenzo Librandi, Oct 21 2014 *) LinearRecurrence[{110,-1},{14,1526},20] (* Harvey P. Dale, Sep 19 2024 *) -
PARI
Vec(-14*x*(x-1)/(x^2-110*x+1) + O(x^20)) \\ Colin Barker, Oct 21 2014
Formula
a(n+2) = 110*a(n+1)-a(n).
G.f.: -14*x*(x-1) / (x^2-110*x+1). - Colin Barker, Oct 21 2014
Extensions
Editing and more terms from Colin Barker, Oct 21 2014