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

0,1

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).

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]

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 *)

Crossrefs

Cf. A041189.

Sequence in context: A089211 A220927 A222858 * A113683 A330790 A060994

Adjacent sequences: A041185 A041186 A041187 * A041189 A041190 A041191

Keyword

nonn,cofr,frac,easy

Author

N. J. A. Sloane.

Status

approved