A042126 Numerators of continued fraction convergents to sqrt(588).

24, 97, 4680, 18817, 907896, 3650401, 176127144, 708158977, 34167758040, 137379191137, 6628368932616, 26650854921601, 1285869405169464, 5170128475599457, 249452036233943400, 1002978273411373057

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 (0,194,0,-1).

Crossrefs

Cf. A042127.

Programs

Magma

I:=[24, 97, 4680, 18817]; [n le 4 select I[n] else 194*Self(n-2)-Self(n-4): n in [1..25]]; // Vincenzo Librandi, Nov 17 2013

Mathematica

Numerator[Convergents[Sqrt[588], 30]] (* or *) CoefficientList[Series[(24 + 97 x + 24 x^2 - x^3)/(1 - 194 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 17 2013 *)
LinearRecurrence[{0,194,0,-1},{24,97,4680,18817},20] (* Harvey P. Dale, Jul 11 2023 *)

Formula

G.f.: (24 + 97*x + 24*x^2 - x^3)/(1 - 194*x^2 + x^4). - Vincenzo Librandi, Nov 17 2013

a(n) = 194*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 17 2013