A041188 Numerators of continued fraction convergents to sqrt(105).

10, 41, 830, 3361, 68050, 275561, 5579270, 22592641, 457432090, 1852321001, 37503852110, 151867729441, 3074858440930, 12451301493161, 252100888304150, 1020854854709761, 20669197982499370, 83697646784707241

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi and Bruno Berselli, Table of n, a(n) for n = 0..100 (first 91 terms from Vincenzo Librandi).
• Index entries for linear recurrences with constant coefficients, signature (0,82,0,-1).

Crossrefs

Cf. A041189.

Programs

Mathematica

Numerator[Convergents[Sqrt[105], 30]] (* Vincenzo Librandi, Oct 30 2013 *)
RecurrenceTable[{a[0] == 10, a[1] == 41, a[2] == 830, a[3] == 3361, a[n] == 82 a[n - 2] - a[n - 4]}, a, {n, 0, 20}] (* Bruno Berselli, Oct 30 2013 *)

Formula

G.f.: (10 + 41*x + 10*x^2 - x^3) / (1 - 82*x^2 + x^4). [Bruno Berselli, Oct 30 2013]

a(n) = 82*a(n-2) - a(n-4). [Bruno Berselli, Oct 30 2013]