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A042012 Numerators of continued fraction convergents to sqrt(530). 2

%I

%S 23,1059,48737,2242961,103224943,4750590339,218630380537,

%T 10061748095041,463059042752423,21310777714706499,980758833919251377,

%U 45136217138000269841,2077246747181931664063,95598486587506856816739,4399607629772497345234057

%N Numerators of continued fraction convergents to sqrt(530).

%H Vincenzo Librandi, <a href="/A042012/b042012.txt">Table of n, a(n) for n = 0..200</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (46,1).

%F a(n)=46*a(n-1)+a(n-2), n>1 ; a(0)=23, a(1)=1059 . G.f.: (23+x)/(1-46*x-x^2). [From _Philippe Deléham_, Nov 23 2008]

%F a(n)=(1/2)*sqrt(530)*{[23+sqrt(530)]^n-[23-sqrt(530)]^n}+(23/2)*{[23+sqrt(530)]^n+[23-sqrt(530)]^n}, with n>=0 [From _Paolo P. Lava_, Nov 28 2008]

%t Numerator[Convergents[Sqrt[530], 30]] (* _Vincenzo Librandi_, Nov 13 2013 *)

%t LinearRecurrence[{46,1},{23,1059},30] (* _Harvey P. Dale_, May 05 2016 *)

%Y Cf. A042013, A040506.

%K nonn,cofr,frac,easy,less

%O 0,1

%A _N. J. A. Sloane_.

%E Additional term from _Colin Barker_, Nov 29 2013

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Last modified March 25 12:11 EDT 2019. Contains 321470 sequences. (Running on oeis4.)