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Numerators of continued fraction convergents to sqrt(560).
2

%I #17 Aug 11 2019 12:17:50

%S 23,24,47,71,3313,3384,6697,10081,470423,480504,950927,1431431,

%T 66796753,68228184,135024937,203253121,9484668503,9687921624,

%U 19172590127,28860511751,1346756130673,1375616642424,2722372773097,4097989415521,191229885887063

%N Numerators of continued fraction convergents to sqrt(560).

%H Vincenzo Librandi, <a href="/A042072/b042072.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_08">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,142,0,0,0,-1).

%F G.f.: (23 +24*x +47*x^2 +71*x^3 +47*x^4 -24*x^5 +23*x^6 -x^7)/((1 -12x^2 +x^4)*(1 +12*x^2 +x^4)). [_Bruno Berselli_, Nov 15 2013]

%t Numerator[Convergents[Sqrt[560], 30]] (* _Vincenzo Librandi_, Nov 15 2013 *)

%t CoefficientList[Series[(23 + 24 x + 47 x^2 + 71 x^3 + 47 x^4 - 24 x^5 + 23 x^6 - x^7)/(1 - 142 x^4 + x^8), {x, 0, 30}], x] (* _Bruno Berselli_, Nov 15 2013 *)

%t LinearRecurrence[{0,0,0,142,0,0,0,-1},{23,24,47,71,3313,3384,6697,10081},30] (* _Harvey P. Dale_, Aug 11 2019 *)

%Y Cf. A042073.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.