%I #20 Jul 09 2025 03:04:13

%S 28,29,115,834,949,26457,27406,218299,682303,900602,51116015,52016617,

%T 207165866,1502177679,1709343545,47654453394,49363796939,393201031967,

%U 1228966892840,1622167924807,92070370682032,93692538606839,373147986502549

%N Numerators of continued fraction convergents to sqrt(827).

%H Vincenzo Librandi, <a href="/A042596/b042596.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, 1801204, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

%F G.f.: -(x^19 -28*x^18 +29*x^17 -115*x^16 +834*x^15 -949*x^14 +26457*x^13 -27406*x^12 +218299*x^11 -682303*x^10 -900602*x^9 -682303*x^8 -218299*x^7 -27406*x^6 -26457*x^5 -949*x^4 -834*x^3 -115*x^2 -29*x -28) / (x^20 -1801204*x^10 +1). - _Colin Barker_, Dec 19 2013

%t Numerator[Convergents[Sqrt[827], 30]] (* _Vincenzo Librandi_, Nov 29 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,0,0,0,1801204,0,0,0,0,0,0,0,0,0,-1},{28,29,115,834,949,26457,27406,218299,682303,900602,51116015,52016617,207165866,1502177679,1709343545,47654453394,49363796939,393201031967,1228966892840,1622167924807},30] (* _Harvey P. Dale_, Jul 06 2021 *)

%Y Cf. A042597, A040798.

%K nonn,frac,easy

%O 0,1

%A _N. J. A. Sloane_

%E More terms from _Colin Barker_, Dec 19 2013