%I #19 Jul 09 2025 01:17:35

%S 1,3,16,83,265,10153,30724,163773,849589,2712540,103926109,314490867,

%T 1676380444,8696393087,27765559705,1063787661877,3219128545336,

%U 17159430388557,89016280488121,284208271852920,10888930610899081,32951000104550163,175643931133649896

%N Denominators of continued fraction convergents to sqrt(373).

%H Vincenzo Librandi, <a href="/A041707/b041707.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_10">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 10236, 0, 0, 0, 0, 1).

%F G.f.: -(x^8 -3*x^7 +16*x^6 -83*x^5 +265*x^4 +83*x^3 +16*x^2 +3*x +1) / (x^10 +10236*x^5 -1). - _Colin Barker_, Nov 22 2013

%F a(n) = 10236*a(n-5) + a(n-10) for n>9. - _Vincenzo Librandi_, Dec 23 2013

%t Denominator[Convergents[Sqrt[373], 30]] (* _Vincenzo Librandi_, Dec 23 2013 *)

%o (Magma) I:=[1,3,16,83,265,10153,30724,163773,849589, 2712540]; [n le 10 select I[n] else 10236*Self(n-5)+Self(n-10): n in [1..40]]; // _Vincenzo Librandi_, Dec 23 2013

%Y Cf. A041706, A040353.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_

%E More terms from _Colin Barker_, Nov 22 2013