A041519 - OEIS

%I #15 Sep 08 2022 08:44:54

%S 1,1,2,3,5,13,31,75,106,181,287,468,15263,15731,30994,46725,77719,

%T 202163,482045,1166253,1648298,2814551,4462849,7277400,237339649,

%U 244617049,481956698,726573747,1208530445,3143634637,7495799719,18135234075,25631033794

%N Denominators of continued fraction convergents to sqrt(276).

%H Vincenzo Librandi, <a href="/A041519/b041519.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 (0,0,0,0,0,0,0,0,0,0,0,15550,0,0,0,0,0,0,0,0,0,0,0,-1).

%F G.f.: -(x^22 -x^21 +2*x^20 -3*x^19 +5*x^18 -13*x^17 +31*x^16 -75*x^15 +106*x^14 -181*x^13 +287*x^12 -468*x^11 -287*x^10 -181*x^9 -106*x^8 -75*x^7 -31*x^6 -13*x^5 -5*x^4 -3*x^3 -2*x^2 -x -1) / ((x^8 -25*x^4 +1)*(x^16 +25*x^12 +624*x^8 +25*x^4 +1)). - _Colin Barker_, Nov 18 2013

%F a(n) = 15550*a(n-12) - a(n-24) for n>23. - _Vincenzo Librandi_, Dec 19 2013

%t Denominator[Convergents[Sqrt[276], 30]] (* _Vincenzo Librandi_, Dec 19 2013 *)

%o (Magma) I:=[1,1,2,3,5,13,31,75,106,181,287,468,15263, 15731,30994,46725,77719,202163,482045,1166253,1648298, 2814551,4462849,7277400]; [n le 24 select I[n] else 15550*Self(n-12)-Self(n-24): n in [1..40]]; // _Vincenzo Librandi_, Dec 19 2013

%Y Cf. A041518, A040259.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 18 2013