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Numerators of continued fraction convergents to sqrt(107).
3

%I #22 Oct 03 2021 04:57:59

%S 10,21,31,300,331,962,19571,40104,59675,577179,636854,1850887,

%T 37654594,77160075,114814669,1110492096,1225306765,3561105626,

%U 72447419285,148455944196,220903363481,2136586215525,2357489579006

%N Numerators of continued fraction convergents to sqrt(107).

%H Vincenzo Librandi, <a href="/A041192/b041192.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_12">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1924,0,0,0,0,0,-1).

%F 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]

%t Numerator[Convergents[Sqrt[107], 30]] (* _Vincenzo Librandi_, Oct 26 2013 *)

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

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.