A042010 Numerators of continued fraction convergents to sqrt(528).

22, 23, 1034, 1057, 47542, 48599, 2185898, 2234497, 100503766, 102738263, 4620987338, 4723725601, 212464913782, 217188639383, 9768765046634, 9985953686017, 449150727231382, 459136680917399

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 (0,46,0,-1).

Crossrefs

Cf. A042011.

Programs

Magma

I:=[22, 23, 1034, 1057]; [n le 4 select I[n] else 46*Self(n-2)-Self(n-4): n in [1..25]]; // Vincenzo Librandi, Nov 13 2013

Mathematica

Numerator[Convergents[Sqrt[528], 30]] (* or *) CoefficientList[Series[-(x^3 - 22 x^2 - 23 x - 22)/(x^4 - 46 x^2 + 1), {x, 0, 30}], x] (* Vincenzo Librandi, Nov 13 2013 *)

Formula

G.f.: -(x^3-22*x^2-23*x-22)/(x^4-46*x^2+1). - Vincenzo Librandi, Nov 13 2013

a(n) = 46*a(n-2)-a(n-4). - Vincenzo Librandi, Nov 13 2013