%I #14 Sep 08 2022 08:44:55

%S 1,3,4,23,73,753,2332,12413,14745,56648,2393961,7238531,9632492,

%T 55400991,175835465,1813755641,5617102388,29899267581,35516369969,

%U 136448377488,5766348224465,17435493050883,23201841275348,133444699427623,423535939558217,4368804095009793

%N Denominators of continued fraction convergents to sqrt(452).

%H Vincenzo Librandi, <a href="/A041861/b041861.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,0,0,0,0,2408706,0,0,0,0,0,0,0,0,0,-1).

%F G.f.: -(x^18 -3*x^17 +4*x^16 -23*x^15 +73*x^14 -753*x^13 +2332*x^12 -12413*x^11 +14745*x^10 -56648*x^9 -14745*x^8 -12413*x^7 -2332*x^6 -753*x^5 -73*x^4 -23*x^3 -4*x^2 -3*x -1) / ((x^10 -1552*x^5 -1)*(x^10 +1552*x^5 -1)). - _Colin Barker_, Nov 26 2013

%F a(n) = 2408706*a(n-10) - a(n-20) for n>19. - _Vincenzo Librandi_, Dec 26 2013

%t Denominator[Convergents[Sqrt[452], 30]] (* _Vincenzo Librandi_, Dec 26 2013 *)

%o (Magma) I:=[1,3,4,23,73,753,2332,12413,14745,56648, 2393961,7238531,9632492,55400991,175835465,1813755641, 5617102388,29899267581,35516369969,136448377488]; [n le 20 select I[n] else 2408706*Self(n-10)-Self(n-20): n in [1..40]]; // _Vincenzo Librandi_, Dec 26 2013

%Y Cf. A041860, A040430.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 26 2013