A042816 - OEIS

%I #17 Oct 08 2023 13:31:58

%S 30,31,61,92,429,8672,35117,43789,78906,122695,7440606,7563301,

%T 15003907,22567208,105272739,2128021988,8617360691,10745382679,

%U 19362743370,30108126049,1825850306310,1855958432359,3681808738669,5537767171028

%N Numerators of continued fraction convergents to sqrt(939).

%H Vincenzo Librandi, <a href="/A042816/b042816.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 245390, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

%F G.f.: -(x^19 -30*x^18 +31*x^17 -61*x^16 +92*x^15 -429*x^14 +8672*x^13 -35117*x^12 +43789*x^11 -78906*x^10 -122695*x^9 -78906*x^8 -43789*x^7 -35117*x^6 -8672*x^5 -429*x^4 -92*x^3 -61*x^2 -31*x -30) / (x^20 -245390*x^10 +1). - _Colin Barker_, Dec 24 2013

%t Numerator[Convergents[Sqrt[939], 30]] (* _Vincenzo Librandi_, Dec 05 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,0,0,0,245390,0,0,0,0,0,0,0,0,0,-1},{30,31,61,92,429,8672,35117,43789,78906,122695,7440606,7563301,15003907,22567208,105272739,2128021988,8617360691,10745382679,19362743370,30108126049},30] (* _Harvey P. Dale_, Oct 08 2023 *)

%Y Cf. A042817, A040908.

%K nonn,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Dec 24 2013