A041089 Denominators of continued fraction convergents to sqrt(52).
1, 4, 5, 14, 19, 90, 1279, 5206, 6485, 18176, 24661, 116820, 1660141, 6757384, 8417525, 23592434, 32009959, 151632270, 2154861739, 8771079226, 10925940965, 30622961156, 41548902121, 196818569640, 2797008877081, 11384854077964, 14181862955045, 39748579988054
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..200
- Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1298,0,0,0,0,0,-1).
Programs
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Mathematica
Table[Denominator[FromContinuedFraction[ContinuedFraction[Sqrt[52], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Jun 23 2011 *) Denominator[Convergents[Sqrt[52], 30]] (* Vincenzo Librandi, Oct 24 2013 *)
Formula
a(n) = 1298*a(n-6)-a(n-12). G.f.: -(x^10-4*x^9+5*x^8-14*x^7+19*x^6-90*x^5-19*x^4-14*x^3-5*x^2-4*x-1)/((x^2-3*x-1)*(x^2+3*x-1)*(x^4-3*x^3+10*x^2+3*x+1)*(x^4+3*x^3+10*x^2-3*x+1)). [Colin Barker, Jul 18 2012]