A042150 Numerators of continued fraction convergents to sqrt(600).

24, 49, 2376, 4801, 232824, 470449, 22814376, 46099201, 2235576024, 4517251249, 219063635976, 442644523201, 21466000749624, 43374646022449, 2103449009827176, 4250272665676801, 206116536962313624, 416483346590304049

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 (0,98,0,-1).

Crossrefs

Cf. A042151.

Programs

Magma

I:=[24,49,2376,4801]; [n le 4 select I[n] else 98*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Nov 18 2013

Mathematica

Numerator[Convergents[Sqrt[600], 30]] (* or *) CoefficientList[Series[(24 + 49 x + 24 x^2 - x^3)/(1 - 98 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 18 2013 *)

Formula

G.f.: (1 + x)*(24 + 25*x - x^2)/((1 - 10*x + x^2)*(1 + 10*x + x^2)). - Vincenzo Librandi, Nov 18 2013

a(n) = 98*a(n-2) - a(n-4). - Vincenzo Librandi, Nov 18 2013