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%I #21 Apr 22 2016 16:12:04
%S 3,6,15,24,57,90,213,336,795,1254,2967,4680,11073,17466,41325,65184,
%T 154227,243270,575583,907896,2148105,3388314,8016837,12645360,
%U 29919243,47193126,111660135,176127144,416721297,657315450,1555225053,2453134656,5804178915
%N Exponents of x in the numerator of cluster variables of rank 2 cluster algebras.
%C These numbers are the exponents of x in the numerator of the cluster algebra A(b,c) of rank 2 with parameters b=2 and c=3. Recall that the algebra A(2,3) is a subalgebra of Q(x,y) generated by the following infinite family of variables:
%C x(n) = (1+x(1-1)^2)/x(n-2) if n is even,
%C x(n) = (1+x(n-1)^3)/x(n-2) if n is odd.
%C with x(0)=x and x(1)=y.
%H Colin Barker, <a href="/A272073/b272073.txt">Table of n, a(n) for n = 2..1000</a>
%H Andrei Zelevinsky, <a href="http://www.ams.org/notices/200711/tx071101494p.pdf">What is a Cluster Algebra?</a>, AMS Notices 54(11): 1494-1495, (2007).
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,4,0,-1).
%F a(n) = 4*a(n-2)-a(n-4), with a(2)=3, a(3)=6, a(4)=15, a(5)=24.
%F G.f.: 3*x^2*(1+x)^2 / (1-4*x^2+x^4). - _Colin Barker_, Apr 22 2016
%o (PARI) Vec(3*x^2*(1+x)^2/(1-4*x^2+x^4) + O(x^50)) \\ _Colin Barker_, Apr 22 2016
%K nonn,easy
%O 2,1
%A _Hector J. Blandin N._, Apr 19 2016
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