A179685 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

A179685

The dimension of the space of invariant tensors in the n-th tensor power of the adjoint representation of the exceptional Lie algebra F4.

1, 0, 1, 1, 5, 16, 80, 436, 2891, 22248, 198774, 2029140, 23310386, 296407466, 4109654354, 61348443380, 976111067870, 16423368282336, 290404344321126, 5370042566624118, 103427555919931446

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,5

COMMENTS

This is known to satisfy a linear recurrence relation with polynomial coefficients. The limit of a(n+1)/a(n) is 52.

LINKS

Table of n, a(n) for n=0..20.

Scott Morrison, Noah Snyder, and Dylan P. Thurston, Towards the quantum exceptional series, arXiv:2402.03637 [math.QA], 2024. See p. 38.

EXAMPLE

The n-th tensor power is the trivial representation for n=0 and is the adjoint representation for n=1. For n=2 every invariant tensor is a scalar multiple of a Killing form.

CROSSREFS

Sequence in context: A372174 A227292 A179683 * A286077 A286072 A002830

Adjacent sequences: A179682 A179683 A179684 * A179686 A179687 A179688

KEYWORD

nonn

AUTHOR

Bruce Westbury, Jul 24 2010

STATUS

approved