A041192 Numerators of continued fraction convergents to sqrt(107).

10, 21, 31, 300, 331, 962, 19571, 40104, 59675, 577179, 636854, 1850887, 37654594, 77160075, 114814669, 1110492096, 1225306765, 3561105626, 72447419285, 148455944196, 220903363481, 2136586215525, 2357489579006

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 (0,0,0,0,0,1924,0,0,0,0,0,-1).

Crossrefs

Cf. A041193 (denominators), A010173 (continued fraction), A177935 (decimal expansion).

Programs

Mathematica

Numerator[Convergents[Sqrt[107], 30]] (* Vincenzo Librandi, Oct 26 2013 *)

Formula

a(n) = 1924*a(n-6)-a(n-12). G.f.: -(x^11-10*x^10+21*x^9-31*x^8+300*x^7-331*x^6-962*x^5-331*x^4-300*x^3-31*x^2-21*x-10)/(x^12-1924*x^6+1). [Colin Barker, Jul 19 2012]