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 A042038 Numerators of continued fraction convergents to sqrt(543). 2

%I #18 Sep 05 2022 21:47:30

%S 23,70,233,769,1002,14797,15799,62194,202381,669337,30991883,93644986,

%T 311926841,1029425509,1341352350,19808358409,21149710759,83257490686,

%U 270922182817,896024039137,41488027983119,125360107988494,417568351948601,1378065163834297

%N Numerators of continued fraction convergents to sqrt(543).

%H Vincenzo Librandi, <a href="/A042038/b042038.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_20">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 0, 0, 0, 0, 0, 0, 1338674, 0, 0, 0, 0, 0, 0, 0, 0, 0, -1).

%F G.f.: -(x^19 -23*x^18 +70*x^17 -233*x^16 +769*x^15 -1002*x^14 +14797*x^13 -15799*x^12 +62194*x^11 -202381*x^10 -669337*x^9 -202381*x^8 -62194*x^7 -15799*x^6 -14797*x^5 -1002*x^4 -769*x^3 -233*x^2 -70*x -23) / (x^20 -1338674*x^10 +1). - _Colin Barker_, Nov 30 2013

%F a(n) = 1338674*a(n-10) - a(n-20). - _Wesley Ivan Hurt_, Sep 05 2022

%t Numerator[Convergents[Sqrt[543], 30]] (* _Vincenzo Librandi_, Nov 14 2013 *)

%Y Cf. A042039, A040519.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.

%E More terms from _Colin Barker_, Nov 30 2013

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Last modified June 23 07:33 EDT 2024. Contains 373629 sequences. (Running on oeis4.)