A042154 Numerators of continued fraction convergents to sqrt(602).

24, 25, 49, 319, 368, 687, 33344, 34031, 67375, 438281, 505656, 943937, 45814632, 46758569, 92573201, 602197775, 694770976, 1296968751, 62949271024, 64246239775, 127195510799, 827419304569, 954614815368, 1782034119937, 86492252572344, 88274286692281

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 (0,0,0,0,0,1374,0,0,0,0,0,-1).

Crossrefs

Cf. A042155.

Programs

Magma

I:=[24,25,49,319,368,687,33344,34031,67375,438281,505656,943937]; [n le 12 select I[n] else 1374*Self(n-6)-Self(n-12): n in [1..30]]; // Vincenzo Librandi, Nov 18 2013

Mathematica

Numerator[Convergents[Sqrt[602], 30]] (* Vincenzo Librandi, Nov 18 2013 *)
LinearRecurrence[{0,0,0,0,0,1374,0,0,0,0,0,-1},{24,25,49,319,368,687,33344,34031,67375,438281,505656,943937},30] (* Harvey P. Dale, Mar 18 2023 *)

Formula

G.f.: (24 +25*x +49*x^2 +319*x^3 +368*x^4 +687*x^5 +368*x^6 -319*x^7 +49*x^8 -25*x^9 +24*x^10 -x^11)/(1 -1374*x^6 +x^12). - Colin Barker, Nov 09 2013

a(n) = 1374*a(n-6) - a(n-12). - Vincenzo Librandi, Nov 18 2013

Extensions

More terms from Colin Barker, Nov 09 2013