A042086 - OEIS

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

%S 23,24,119,381,1643,2024,94747,96771,481831,1542264,6650887,8193151,

%T 383535833,391728984,1950451769,6243084291,26922788933,33165873224,

%U 1552552957237,1585718830461,7895428279081

%N Numerators of continued fraction convergents to sqrt(567).

%H Vincenzo Librandi, <a href="/A042086/b042086.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 (0,0,0,0,0,4048,0,0,0,0,0,-1).

%F G.f.: -(x^11 - 23*x^10 + 24*x^9 - 119*x^8 + 381*x^7 - 1643*x^6 - 2024*x^5 - 1643*x^4 - 381*x^3 - 119*x^2 - 24*x - 23)/(x^12 - 4048*x^6 + 1). - _Vincenzo Librandi_, Nov 16 2013

%F a(n) = 4048*a(n-6) - a(n-12). - _Vincenzo Librandi_, Nov 16 2013

%t Numerator[Convergents[Sqrt[567], 30]] (* or *) CoefficientList[Series[-(x^11 - 23 x^10 + 24 x^9 - 119 x^8 + 381 x^7 - 1643 x^6 - 2024 x^5 - 1643 x^4 - 381 x^3 - 119 x^2 - 24 x - 23)/(x^12 - 4048 x^6 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 16 2013 *)

%o (Magma) I:=[23, 24, 119, 381, 1643, 2024, 94747, 96771, 481831, 1542264, 6650887, 8193151]; [n le 12 select I[n] else 4048*Self(n-6)-Self(n-12): n in [1..30]]; // _Vincenzo Librandi_, Nov 16 2013

%Y Cf. A042087.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.