A041371 Denominators of continued fraction convergents to sqrt(200).
1, 7, 197, 1386, 39005, 274421, 7722793, 54333972, 1529074009, 10757852035, 302748930989, 2130000368958, 59942759261813, 421729315201649, 11868363584907985, 83500274409557544, 2349876047052519217, 16532632603777192063, 465263588952813896981
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,198,0,-1).
Programs
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Magma
I:=[1,7,197,1386]; [n le 4 select I[n] else 198*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 16 2013
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Mathematica
Denominator[Convergents[Sqrt[200], 30]] (* Vincenzo Librandi, Dec 16 2013 *)
Formula
G.f.: -(x^2-7*x-1) / ((x^2-14*x-1)*(x^2+14*x-1)). - Colin Barker, Nov 16 2013
a(n) = 198*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 16 2013
Extensions
More terms from Colin Barker, Nov 16 2013