A042300 Numerators of continued fraction convergents to sqrt(677).

26, 1353, 70382, 3661217, 190453666, 9907251849, 515367549814, 26809019842177, 1394584399343018, 72545197785679113, 3773744869254656894, 196307278399027837601, 10211752221618702212146, 531207422802571542869193, 27632997737955338931410182

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

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 (52, 1).

Crossrefs

Cf. A042301, A040650.

Programs

Magma

I:=[26,1353]; [n le 2 select I[n] else 52*Self(n-1)+Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 21 2013

Mathematica

Numerator[Convergents[Sqrt[677], 30]] (* or *) LinearRecurrence[{52, 1}, {26, 1353}, 30] (* Harvey P. Dale, Nov 09 2011 *)

Formula

a(n) = 52*a(n-1)+a(n-2) for n>1, a(0)=26, a(1)=1353. G.f.: (26+x)/(1-52*x -x^2). [Philippe Deléham, Nov 23 2008]

Extensions

Additional term from Colin Barker, Dec 07 2013