A041198 Numerators of continued fraction convergents to sqrt(110).
10, 21, 430, 881, 18050, 36981, 757670, 1552321, 31804090, 65160501, 1335014110, 2735188721, 56038788530, 114812765781, 2352294104150, 4819400974081, 98740313585770, 202300028145621, 4144740876498190, 8491781781142001, 173980376499338210, 356452534779818421
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..100
- Index entries for linear recurrences with constant coefficients, signature (0,42,0,-1).
Crossrefs
Cf. A041199.
Programs
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Mathematica
Numerator[Convergents[Sqrt[110], 30]] (* Vincenzo Librandi, Oct 30 2013 *) LinearRecurrence[{0,42,0,-1},{10,21,430,881},30] (* Harvey P. Dale, Mar 04 2015 *)
Formula
G.f.: -(x+1)*(x^2-11*x-10) / (x^4-42*x^2+1). - Colin Barker, Nov 05 2013
a(0)=10, a(1)=21, a(2)=430, a(3)=881, a(n)=42*a(n-2)-a(n-4). - Harvey P. Dale, Mar 04 2015
Extensions
More terms from Colin Barker, Nov 05 2013