A272073 Exponents of x in the numerator of cluster variables of rank 2 cluster algebras.

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

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(n-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