A041833 Denominators of continued fraction convergents to sqrt(437).
1, 1, 10, 21, 199, 220, 8999, 9219, 91970, 193159, 1830401, 2023560, 82772801, 84796361, 845940050, 1776676461, 16836028199, 18612704660, 761344214599, 779956919259, 7780956487930, 16341869895119, 154857785544001, 171199655439120, 7002844003108801
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0, 0, 0, 0, 0, 9198, 0, 0, 0, 0, 0, -1).
Programs
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Magma
I:=[1,1,10,21,199,220,8999,9219,91970,193159, 1830401,2023560]; [n le 12 select I[n] else 9198*Self(n-6)-Self(n-12): n in [1..40]]; // Vincenzo Librandi, Dec 25 2013
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Mathematica
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[437], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 23 2011 *) Denominator[Convergents[Sqrt[437], 30]] (* Vincenzo Librandi, Dec 25 2013 *)
Formula
G.f.: -(x^10 -x^9 +10*x^8 -21*x^7 +199*x^6 -220*x^5 -199*x^4 -21*x^3 -10*x^2 -x -1) / ((x^4 -21*x^2 +1)*(x^8 +21*x^6 +440*x^4 +21*x^2 +1)). - Colin Barker, Nov 25 2013
a(n) = 9198*a(n-6) - a(n-12) for n>11. - Vincenzo Librandi, Dec 25 2013