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

0,1

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).

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]

Mathematica

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

Prog

(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

Crossrefs

Cf. A042301, A040650.

Sequence in context: A106710 A114052 A042303 * A282884 A080163 A368852

Adjacent sequences: A042297 A042298 A042299 * A042301 A042302 A042303

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Extensions

Additional term from Colin Barker, Dec 07 2013

Status

approved