A041048 Numerators of continued fraction convergents to sqrt(30).

5, 11, 115, 241, 2525, 5291, 55435, 116161, 1217045, 2550251, 26719555, 55989361, 586613165, 1229215691, 12878770075, 26986755841, 282746328485, 592479412811, 6207540456595, 13007560326001, 136283143716605, 285573847759211, 2992021621308715, 6269617090376641

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• cofr
• frac
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for linear recurrences with constant coefficients, signature (0,22,0,-1).

Crossrefs

Cf. A010485, A041049.

Programs

Mathematica

Table[Numerator[FromContinuedFraction[ContinuedFraction[Sqrt[30], n]]], {n, 1, 50}] (* Vladimir Joseph Stephan Orlovsky, Mar 18 2011 *)
Numerator[Convergents[Sqrt[30], 30]] (* Harvey P. Dale, May 06 2012 *)

Formula

G.f.: (5+11*x+5*x^2-x^3)/(1-22*x^2+x^4). - Colin Barker, Jan 02 2012

a(n) = 22*a(n-2) - a(n-4). - Wesley Ivan Hurt, Jun 16 2023

Extensions

More terms from Harvey P. Dale, Apr 04 2013