A042030 Numerators of continued fraction convergents to sqrt(539).

23, 93, 116, 209, 325, 534, 859, 3970, 183479, 737886, 921365, 1659251, 2580616, 4239867, 6820483, 31521799, 1456823237, 5858814747, 7315637984, 13174452731, 20490090715, 33664543446, 54154634161, 250283080090, 11567176318301, 46518988353294, 58086164671595

Offset

0,1

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, 0, 0, 7940, 0, 0, 0, 0, 0, 0, 0, -1).

Formula

G.f.: -(x^15 -23*x^14 +93*x^13 -116*x^12 +209*x^11 -325*x^10 +534*x^9 -859*x^8 -3970*x^7 -859*x^6 -534*x^5 -325*x^4 -209*x^3 -116*x^2 -93*x -23) / (x^16 -7940*x^8 +1). - Colin Barker, Nov 29 2013

a(n) = 7940*a(n-8) - a(n-16). - Wesley Ivan Hurt, Sep 05 2022

Mathematica

Numerator[Convergents[Sqrt[539], 30]]  (* Vincenzo Librandi, Nov 14 2013 *)

Crossrefs

Cf. A042031, A040515.

Sequence in context: A306138 A317371 A244632 * A042032 A257976 A183011

Adjacent sequences: A042027 A042028 A042029 * A042031 A042032 A042033

Keyword

nonn,cofr,frac,easy,less

Author

N. J. A. Sloane.

Extensions

More terms from Colin Barker, Nov 29 2013

Status

approved