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A042196 Numerators of continued fraction convergents to sqrt(623). 2

%I

%S 24,25,599,624,30551,31175,747576,778751,38127624,38906375,932974249,

%T 971880624,47583244201,48555124825,1164351115176,1212906240001,

%U 59383850635224,60596756875225,1453109258765399

%N Numerators of continued fraction convergents to sqrt(623).

%H Vincenzo Librandi, <a href="/A042196/b042196.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 (0,0,0,1248,0,0,0,-1).

%F G.f.: (24 +25*x +599*x^2 +624*x^3 +599*x^4 -25*x^5 +24*x^6 -x^7)/(1 -1248*x^4 +x^8). - _Vincenzo Librandi_, Nov 18 2013

%F a(n) = 1248*a(n-4) - a(n-8). - _Vincenzo Librandi_, Nov 18 2013

%t Numerator[Convergents[Sqrt[623], 30]] (* or *) CoefficientList[Series[(24 + 25 x + 599 x^2 + 624 x^3 + 599 x^4 - 25 x^5 + 24 x^6 - x^7)/(1 - 1248 x^4 + x^8), {x, 0, 30}], x] (* _Vincenzo Librandi_, Nov 18 2013 *)

%o (MAGMA) I:=[24, 25, 599, 624, 30551, 31175, 747576, 778751]; [n le 8 select I[n] else 1248*Self(n-4)-Self(n-8): n in [1..30]]; // _Vincenzo Librandi_, Nov 18 2013

%Y Cf. A042197.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.

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Last modified January 24 04:35 EST 2020. Contains 331183 sequences. (Running on oeis4.)