A155888 a(n) = dimension of the space of n-boxes in the unshaded subfactor planar algebra of type E8.

1, 1, 2, 5, 14, 43, 143, 506, 1870, 7107, 27474, 107274, 421268, 1659725, 6551041, 25884007, 102330007, 404682554, 1600678795, 6331951858, 25049290301, 99098453901, 392054049162, 1551062360070, 6136418173129, 24277388110318

Offset

0,3

Comments

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.

Links

Table of n, a(n) for n=0..25.

V. Jones, Planar Algebras I, arXiv:math/9909027v1 [math.QA]

Formula

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)

Crossrefs

Sequence in context: A110489 A005425 A035349 * A366099 A254314 A249562

Adjacent sequences: A155885 A155886 A155887 * A155889 A155890 A155891

Keyword

easy,nonn

Author

Stephen Bigelow (bigelow(AT)math.ucsb.edu), Jan 29 2009

Status

approved