A041160 Numerators of continued fraction convergents to sqrt(90).

9, 19, 351, 721, 13329, 27379, 506151, 1039681, 19220409, 39480499, 729869391, 1499219281, 27715816449, 56930852179, 1052471155671, 2161873163521, 39966188099049, 82094249361619, 1517662676608191

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..100
• Index entries for linear recurrences with constant coefficients, signature (0,38,0,-1).

Crossrefs

Cf. A010541, A041161.

Programs

Mathematica

Numerator[Convergents[Sqrt[90], 30]] (* Vincenzo Librandi, Oct 29 2013 *)
Table[(2 + (-1)^n) ((3 - Sqrt[10])^(n + 1) + (3 + Sqrt[10])^(n + 1))/2, {n, 0, 30}] (* Bruno Berselli, Oct 30 2013 *)
LinearRecurrence[{0,38,0,-1},{9,19,351,721},30] (* Harvey P. Dale, May 12 2018 *)

Formula

G.f.: (1 + x)*(9 + 10*x - x^2) / (1 - 38*x^2 + x^4). [Bruno Berselli, Oct 30 2013]

a(n) = (2+(-1)^n)*((3-sqrt(10))^(n+1)+(3+sqrt(10))^(n+1))/2. [Bruno Berselli, Oct 30 2013]