%I
%S 1,1,2,5,14,43,143,506,1870,7107,27474,107274,421268,1659725,6551041,
%T 25884007,102330007,404682554,1600678795,6331951858,25049290301,
%U 99098453901,392054049162,1551062360070,6136418173129,24277388110318
%N a(n) = dimension of the space of nboxes in the unshaded subfactor planar algebra of type E8.
%C a(n) is also the number of paths of length 2n in the E8 graph that begin and end at the vertex farthest from the trivalent vertex.
%H V. Jones, <a href="http://arxiv.org/abs/math/9909027">Planar Algebras I</a>, arXiv:math/9909027v1 [math.QA]
%F G.f.: (1  8*x + 21*x^2  21*x^3 + 6*x^4)/(1  9*x + 28*x^2  36*x^3 + 17*x^4  2*x^5)
%K easy,nonn
%O 0,3
%A Stephen Bigelow (bigelow(AT)math.ucsb.edu), Jan 29 2009
