A042858 Numerators of continued fraction convergents to sqrt(960).

30, 31, 1890, 1921, 117150, 119071, 7261410, 7380481, 450090270, 457470751, 27898335330, 28355806081, 1729246700190, 1757602506271, 107185397076450, 108942999582721, 6643765372039710, 6752708371622431, 411806267669385570, 418558976041008001, 25525344830129865630

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,62,0,-1).

Crossrefs

Cf. A042859.

Programs

Magma

I:=[ 30, 31, 1890, 1921]; [n le 4 select I[n] else 62*Self(n-2)-Self(n-4): n in [1..30]]; // Vincenzo Librandi, Dec 08 2013

Mathematica

Numerator[Convergents[Sqrt[960], 30]] (* Vincenzo Librandi, Dec 07 2013 *)
CoefficientList[Series[(30 + 31 x + 30 x^2 - x^3)/(1 - 62 x^2 + x^4), {x, 0, 30}], x] (* Vincenzo Librandi, Dec 08 2013 *)

Formula

G.f.: (30 + 31*x + 30*x^2 - x^3)/(1 - 62*x^2 + x^4). - Vincenzo Librandi, Dec 08 2013

a(n) = 62*a(n-2) - a(n-4). - Vincenzo Librandi, Dec 08 2013

Extensions

More terms from Vincenzo Librandi, Dec 08 2013