A041909 - OEIS

%I #16 Sep 08 2022 08:44:55

%S 1,1,5,11,115,241,1079,1320,56519,57839,287875,633589,6623765,

%T 13881119,62148241,76029360,3255381361,3331410721,16581024245,

%U 36493459211,381515616355,799524691921,3579614384039,4379139075960,187503455574359,191882594650319

%N Denominators of continued fraction convergents to sqrt(476).

%H Vincenzo Librandi, <a href="/A041909/b041909.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_16">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 57598, 0, 0, 0, 0, 0, 0, 0, -1).

%F G.f.: -(x^14 -x^13 +5*x^12 -11*x^11 +115*x^10 -241*x^9 +1079*x^8 -1320*x^7 -1079*x^6 -241*x^5 -115*x^4 -11*x^3 -5*x^2 -x -1) / ((x^8 -240*x^4 +1)*(x^8 +240*x^4 +1)). - _Colin Barker_, Nov 27 2013

%F a(n) = 57598*a(n-8) - a(n-16) for n>15. - _Vincenzo Librandi_, Dec 27 2013

%t Denominator[Convergents[Sqrt[476], 30]] (* _Vincenzo Librandi_, Dec 27 2013 *)

%o (Magma) I:=[1,1,5,11,115,241,1079,1320,56519,57839, 287875,633589,6623765,13881119,62148241,76029360]; [n le 16 select I[n] else 57598*Self(n-8)-Self(n-16): n in [1..30]]; // _Vincenzo Librandi_, Dec 27 2013

%Y Cf. A041908, A040454.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 27 2013