A042200 Numerators of continued fraction convergents to sqrt(626).

25, 1251, 62575, 3130001, 156562625, 7831261251, 391719625175, 19593812520001, 980082345625225, 49023711093781251, 2452165637034687775, 122657305562828170001, 6135317443778443187825, 306888529494484987561251

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 (50, 1).

Crossrefs

Cf. A042201.

Programs

Magma

I:=[25,1251]; [n le 2 select I[n] else 50*Self(n-1)+Self(n-2): n in [1..30]]; // Vincenzo Librandi, Nov 19 2013

Mathematica

Numerator[Convergents[Sqrt[626], 30]] (* Harvey P. Dale, Jul 15 2012 *)
CoefficientList[Series[(25 + x)/(1 - 50 x - x^2), {x, 0, 20}], x] (* Vincenzo Librandi, Nov 19 2013 *)

Formula

a(n) = 50*a(n-1)+a(n-2) for n>1; a(0)=25, a(1)=1251. G.f.: (25+x)/(1-50*x-x^2). [Philippe Deléham, Nov 23 2008]