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

0,2

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).

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]

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 *)

Crossrefs

Cf. A010505, A041088.

Sequence in context: A041669 A300278 A129720 * A042321 A050164 A188021

Adjacent sequences: A041086 A041087 A041088 * A041090 A041091 A041092

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved