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 A272073 Exponents of x in the numerator of cluster variables of rank 2 cluster algebras. 1
 3, 6, 15, 24, 57, 90, 213, 336, 795, 1254, 2967, 4680, 11073, 17466, 41325, 65184, 154227, 243270, 575583, 907896, 2148105, 3388314, 8016837, 12645360, 29919243, 47193126, 111660135, 176127144, 416721297, 657315450, 1555225053, 2453134656, 5804178915 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,1 COMMENTS 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: x(n) = (1+x(1-1)^2)/x(n-2) if n is even, x(n) = (1+x(n-1)^3)/x(n-2) if n is odd. with x(0)=x and x(1)=y. LINKS Colin Barker, Table of n, a(n) for n = 2..1000 Andrei Zelevinsky, What is a Cluster Algebra?, AMS Notices 54(11): 1494-1495, (2007). Index entries for linear recurrences with constant coefficients, signature (0,4,0,-1). FORMULA a(n) = 4*a(n-2)-a(n-4), with a(2)=3, a(3)=6, a(4)=15, a(5)=24. G.f.: 3*x^2*(1+x)^2 / (1-4*x^2+x^4). - Colin Barker, Apr 22 2016 PROG (PARI) Vec(3*x^2*(1+x)^2/(1-4*x^2+x^4) + O(x^50)) \\ Colin Barker, Apr 22 2016 CROSSREFS Sequence in context: A280465 A282263 A118035 * A282008 A281212 A062878 Adjacent sequences:  A272070 A272071 A272072 * A272074 A272075 A272076 KEYWORD nonn,easy AUTHOR Hector J. Blandin N., Apr 19 2016 STATUS approved

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Last modified February 22 08:42 EST 2020. Contains 332133 sequences. (Running on oeis4.)