login
Numerators of continued fraction convergents to sqrt(677).
3

%I #29 Dec 26 2023 07:04:05

%S 26,1353,70382,3661217,190453666,9907251849,515367549814,

%T 26809019842177,1394584399343018,72545197785679113,

%U 3773744869254656894,196307278399027837601,10211752221618702212146,531207422802571542869193,27632997737955338931410182

%N Numerators of continued fraction convergents to sqrt(677).

%H Vincenzo Librandi, <a href="/A042300/b042300.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#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (52, 1).

%F a(n) = 52*a(n-1)+a(n-2) for n>1, a(0)=26, a(1)=1353. G.f.: (26+x)/(1-52*x -x^2). [_Philippe Deléham_, Nov 23 2008]

%t Numerator[Convergents[Sqrt[677], 30]] (* or *) LinearRecurrence[{52, 1}, {26, 1353}, 30] (* _Harvey P. Dale_, Nov 09 2011 *)

%o (Magma) I:=[26,1353]; [n le 2 select I[n] else 52*Self(n-1)+Self(n-2): n in [1..30]]; // _Vincenzo Librandi_, Nov 21 2013

%Y Cf. A042301, A040650.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_.

%E Additional term from _Colin Barker_, Dec 07 2013