%I #17 Sep 08 2022 08:44:54
%S 1,1,2,9,11,42,53,254,307,561,20503,21064,41567,187332,228899,874029,
%T 1102928,5285741,6388669,11674410,426667429,438341839,865009268,
%U 3898378911,4763388179,18188543448,22951931627,109996269956,132948201583,242944471539
%N Denominators of continued fraction convergents to sqrt(344).
%H Vincenzo Librandi, <a href="/A041651/b041651.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, 20810, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).
%F G.f.: -(x^18 -x^17 +2*x^16 -9*x^15 +11*x^14 -42*x^13 +53*x^12 -254*x^11 +307*x^10 -561*x^9 -307*x^8 -254*x^7 -53*x^6 -42*x^5 -11*x^4 -9*x^3 -2*x^2 -x -1) / (x^20 -20810*x^10 +1). - _Colin Barker_, Nov 20 2013
%F a(n) = 20810*a(n-10) - a(n-20) for n>19. - _Vincenzo Librandi_, Dec 22 2013
%t Denominator[Convergents[Sqrt[344], 30]] (* _Vincenzo Librandi_, Dec 22 2013 *)
%o (Magma) I:=[1,1,2,9,11,42,53,254,307,561,20503,21064, 41567,187332,228899,874029,1102928,5285741,6388669, 11674410]; [n le 20 select I[n] else 20810*Self(n-10)-Self(n-20): n in [1..40]]; // _Vincenzo Librandi_, Dec 22 2013
%Y Cf. A041650, A040325.
%K nonn,frac,easy
%O 0,3
%A _N. J. A. Sloane_.
%E More terms from _Colin Barker_, Nov 20 2013
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