A041832 Numerators of continued fraction convergents to sqrt(437).

20, 21, 209, 439, 4160, 4599, 188120, 192719, 1922591, 4037901, 38263700, 42301601, 1730327740, 1772629341, 17683991809, 37140612959, 351949508440, 389090121399, 15915554364400, 16304644485799, 162657354736591, 341619353958981, 3237231540367420

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy
• less

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).

Crossrefs

Cf. A041833, A040416.

Programs

Mathematica

Numerator[Convergents[Sqrt[437], 30]] (* Vincenzo Librandi, Nov 09 2013 *)
LinearRecurrence[{0,0,0,0,0,9198,0,0,0,0,0,-1},{20,21,209,439,4160,4599,188120,192719,1922591,4037901,38263700,42301601},30] (* Harvey P. Dale, Jul 09 2024 *)

Formula

G.f.: -(x^11 -20*x^10 +21*x^9 -209*x^8 +439*x^7 -4160*x^6 -4599*x^5 -4160*x^4 -439*x^3 -209*x^2 -21*x -20) / ((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). - Wesley Ivan Hurt, May 04 2021

Extensions

More terms from Colin Barker, Nov 25 2013