A042104 Numerators of continued fraction convergents to sqrt(577).

24, 1153, 55368, 2658817, 127678584, 6131230849, 294426759336, 14138615678977, 678947979350232, 32603641624490113, 1565653745954875656, 75183983447458521601, 3610396859223963912504, 173374233226197726321793

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
• Tanya Khovanova, Recursive Sequences
• Index entries for linear recurrences with constant coefficients, signature (48, 1).

Crossrefs

Cf. A042105.

Programs

Mathematica

Numerator[Convergents[Sqrt[577], 30]] (* Vincenzo Librandi, Nov 16 2013 *)
LinearRecurrence[{48,1},{24,1153},20] (* Harvey P. Dale, Sep 02 2024 *)

Formula

a(n) = 48*a(n-1)+a(n-2)for n>1, a(0)=24, a(1)=1153. G.f.: (24+x)/(1-48*x-x^2). [Philippe Deléham, Nov 23 2008]