A042677 - OEIS

%I #18 Sep 08 2022 08:44:55

%S 1,2,13,249,511,9958,60259,130476,7627867,15386210,99945127,

%T 1914343623,3928632373,76558358710,463278784633,1003115927976,

%U 58644002607241,118291121142458,768390729461989,14717714980920249,30203820691302487,588590308115667502

%N Denominators of continued fraction convergents to sqrt(868).

%H Vincenzo Librandi, <a href="/A042677/b042677.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, 7688126, 0, 0, 0, 0, 0, 0, 0, -1).

%F G.f.: -(x^14 -2*x^13 +13*x^12 -249*x^11 +511*x^10 -9958*x^9 +60259*x^8 -130476*x^7 -60259*x^6 -9958*x^5 -511*x^4 -249*x^3 -13*x^2 -2*x -1) / (x^16 -7688126*x^8 +1). - _Colin Barker_, Dec 20 2013

%F a(n) = 7688126*a(n-8) - a(n-16) for n>15. - _Vincenzo Librandi_, Dec 20 2013

%t Denominator[Convergents[Sqrt[868], 30]] (* _Harvey P. Dale_, Sep 24 2013 *)

%t CoefficientList[Series[-(x^14 - 2 x^13 + 13 x^12 - 249 x^11 + 511 x^10 - 9958 x^9 + 60259 x^8 - 130476 x^7 - 60259 x^6 - 9958 x^5 - 511 x^4 - 249 x^3 - 13 x^2 - 2 x - 1)/(x^16 - 7688126 x^8 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Dec 20 2013 *)

%o (Magma) I:=[1,2,13,249,511,9958,60259,130476,7627867, 15386210,99945127,1914343623,3928632373,76558358710, 463278784633,1003115927976]; [n le 16 select I[n] else 7688126*Self(n-8)-Self(n-16): n in [1..40]]; // _Vincenzo Librandi_, Dec 20 2013

%Y Cf. A042676, A040838.

%K nonn,frac,easy

%O 0,2

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Dec 20 2013