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Denominators of continued fraction convergents to sqrt(774).
2

%I #19 Sep 08 2022 08:44:55

%S 1,1,5,6,11,28,39,67,307,374,20503,20877,104011,124888,228899,582686,

%T 811585,1394271,6388669,7782940,426667429,434450369,2164468905,

%U 2598919274,4763388179,12125695632,16889083811,29014779443,132948201583,161962981026,8878949176987

%N Denominators of continued fraction convergents to sqrt(774).

%H Vincenzo Librandi, <a href="/A042493/b042493.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 +5*x^16 -6*x^15 +11*x^14 -28*x^13 +39*x^12 -67*x^11 +307*x^10 -374*x^9 -307*x^8 -67*x^7 -39*x^6 -28*x^5 -11*x^4 -6*x^3 -5*x^2 -x -1) / (x^20 -20810*x^10 +1). - _Colin Barker_, Dec 15 2013

%F a(n) = 20810*a(n-10) - a(n-20). - _Vincenzo Librandi_, Dec 15 2013

%t Denominator[Convergents[Sqrt[774], 30]] (* _Vincenzo Librandi_, Dec 15 2013 *)

%t LinearRecurrence[{0,0,0,0,0,0,0,0,0,20810,0,0,0,0,0,0,0,0,0,-1},{1,1,5,6,11,28,39,67,307,374,20503,20877,104011,124888,228899,582686,811585,1394271,6388669,7782940,426667429},40] (* _Harvey P. Dale_, Jun 29 2015 *)

%o (Magma) I:=[1,1,5,6,11,28,39,67,307,374,20503,20877, 104011,124888,228899,582686,811585,1394271,6388669, 7782940]; [n le 20 select I[n] else 20810*Self(n-10)-Self(n-20): n in [1..40]]; // _Vincenzo Librandi_, Dec 15 2013

%Y Cf. A042492, A040746.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Dec 15 2013