

A179685


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


0



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


EXAMPLE

The nth 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: A179663 A227292 A179683 * A002830 A196015 A160739
Adjacent sequences: A179682 A179683 A179684 * A179686 A179687 A179688


KEYWORD

nonn


AUTHOR

Bruce Westbury (Bruce.Westbury(AT)warwick.ac.uk), Jul 24 2010


STATUS

approved



