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 A042381 Denominators of continued fraction convergents to sqrt(717). 2

%I #15 Sep 08 2022 08:44:55

%S 1,1,4,9,112,121,2048,2169,28076,58321,203039,261360,13793759,

%T 14055119,55959116,125973351,1567639328,1693612679,28665442192,

%U 30359054871,392974100644,816307256159,2841895869121,3658203125280,193068458383681,196726661508961

%N Denominators of continued fraction convergents to sqrt(717).

%H Vincenzo Librandi, <a href="/A042381/b042381.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_24">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 13996798, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

%F G.f.: -(x^22 -x^21 +4*x^20 -9*x^19 +112*x^18 -121*x^17 +2048*x^16 -2169*x^15 +28076*x^14 -58321*x^13 +203039* x^12 -261360*x^11 -203039*x^10 -58321*x^9 -28076*x^8 -2169*x^7 -2048*x^6 -121*x^5 -112*x^4 -9*x^3 -4*x^2 -x -1)/(x^24 -13996798*x^12 +1). - _Vincenzo Librandi_, Jan 21 2014

%F a(n) = 13996798*a(n-12) - a(n-24) for n>23. - _Vincenzo Librandi_, Jan 21 2014

%t Denominator[Convergents[Sqrt[717], 30]] (* _Harvey P. Dale_, Feb 12 2013 *)

%t CoefficientList[Series[-(x^22 - x^21 + 4 x^20 - 9 x^19 + 112 x^18 - 121 x^17 + 2048 x^16 -2169 x^15 + 28076 x^14 - 58321 x^13 + 203039 x^12 - 261360 x^11 - 203039 x^10 - 58321 x^9 - 28076 x^8 - 2169 x^7 - 2048 x^6 - 121 x^5 - 112 x^4 - 9 x^3 - 4 x^2 - x - 1)/(x^24 - 13996798 x^12 + 1), {x, 0, 30}], x] (* _Vincenzo Librandi_, Jan 21 2014 *)

%o (Magma) I:=[1,1,4,9,112,121,2048,2169,28076,58321,203039, 261360,13793759,14055119,55959116,125973351,1567639328, 1693612679,28665442192,30359054871,392974100644, 816307256159,2841895869121,3658203125280]; [n le 24 select I[n] else 13996798*Self(n-12)-Self(n-24): n in [1..30]]; // _Vincenzo Librandi_, Jan 21 2014

%Y Cf. A042380.

%K nonn,frac,easy

%O 0,3

%A _N. J. A. Sloane_.

%E More terms from _Vincenzo Librandi_, Jan 21 2014

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Last modified November 28 22:01 EST 2023. Contains 367420 sequences. (Running on oeis4.)