%I #21 Sep 08 2022 08:44:50

%S 1,2,13,29,194,433,2897,6466,43261,96557,646018,1441889,9647009,

%T 21531778,144059117,321534781,2151239746,4801489937,32124537073,

%U 71700814274,479716816349,1070710724173,7163627708162,15988960048321

%N Markov numbers satisfying region 5 (x=5) of the equation x^2 + y^2 + z^2 = 3xyz.

%C Positive values of x (or y) satisfying x^2 - 15xy + y^2 + 25 = 0. - _Colin Barker_, Feb 11 2014

%H Vincenzo Librandi, <a href="/A030452/b030452.txt">Table of n, a(n) for n = 1..200</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/MarkovNumber.html">Markov Number.</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (0,15,0,-1).

%F a(n) = 15*a(n-2)-a(n-4).

%F G.f.: -x*(x-1)*(x^2+3*x+1) / (x^4-15*x^2+1). - _Colin Barker_, Feb 11 2014

%t CoefficientList[Series[(1 - x) (x^2 + 3 x + 1)/(x^4 - 15 x^2 + 1), {x, 0, 40}], x] (* _Vincenzo Librandi_, Feb 12 2014 *)

%o (PARI) Vec(-x*(x-1)*(x^2+3*x+1)/(x^4-15*x^2+1) + O(x^100)) \\ _Colin Barker_, Feb 11 2014

%o (Magma) I:=[1,2,13,29]; [n le 4 select I[n] else 15*Self(n-2)-Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Feb 12 2014

%K nonn,easy

%O 1,2

%A Mark Milhet (mm992395(AT)shellus.com)

%E More terms from _James A. Sellers_, May 01 2000

%E Offset changed to 1 by _Colin Barker_, Feb 11 2014