A041684 - OEIS

%I #27 Dec 26 2023 07:03:05

%S 19,723,27493,1045457,39754859,1511730099,57485498621,2185960677697,

%T 83123991251107,3160897628219763,120197233863602101,

%U 4570655784445099601,173805117042777386939,6609165103409985803283,251322079046622237911693,9556848168875055026447617

%N Numerators of continued fraction convergents to sqrt(362).

%H Vincenzo Librandi, <a href="/A041684/b041684.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 (38,1).

%F From _Philippe Deléham_, Nov 23 2008: (Start)

%F a(n) = 38*a(n-1) + a(n-2), n > 1; a(0)=19, a(1)=723.

%F G.f.: (19+x)/(1-38*x-x^2). (End)

%t Numerator[Convergents[Sqrt[362], 30]] (* _Vincenzo Librandi_, Nov 06 2013 *)

%t LinearRecurrence[{38,1},{19,723},20] (* _Harvey P. Dale_, Feb 10 2019 *)

%Y Cf. A041685.

%K nonn,cofr,frac,easy

%O 0,1

%A _N. J. A. Sloane_

%E Additional term from _Colin Barker_, Nov 09 2013