A179683 The dimension of the space of invariant tensors in the n-th tensor power of the adjoint representation of the exceptional Lie algebra E7.

1, 0, 1, 1, 5, 16, 80, 436, 2877, 21828, 189877, 1865175, 20468437, 248376198, 3303397123, 47785692843, 746841034620, 12538089887528, 224955746518560, 4294093811333388, 86859002770470072, 1855099612560598420, 41698660497526383757

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 133.

Links

Bruce Westbury, Table of n, a(n) for n = 0..32

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: A203852 A179663 A227292 * A179685 A286077 A286072

Adjacent sequences: A179680 A179681 A179682 * A179684 A179685 A179686

Keyword

nonn

Author

Bruce Westbury, Jul 24 2010

Extensions

More terms from Bruce Westbury, Nov 08 2013

Status

approved