cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A179684 The dimension of the space of invariant tensors in the n-th tensor power of the adjoint representation of the exceptional Lie algebra E6.

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%I A179684 #9 Jan 13 2025 11:09:59
%S A179684 1,0,1,1,5,17,90,542,3962,33554,324489,3520885,42300709,556530474,
%T A179684 7945317484,122145525208,2008827010000,35143981009968
%N A179684 The dimension of the space of invariant tensors in the n-th tensor power of the adjoint representation of the exceptional Lie algebra E6.
%C A179684 This is known to satisfy a linear recurrence relation with polynomial coefficients. The limit of a(n+1)/a(n) is 78.
%H A179684 Jacob L. Bourjaily, Michael Plesser, and Cristian Vergu, <a href="https://arxiv.org/abs/2412.21189">The Many Colours of Amplitudes</a>, arXiv:2412.21189 [hep-th], 2024. See p. 53.
%e A179684 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.
%K A179684 nonn,more
%O A179684 0,5
%A A179684 _Bruce Westbury_, Jul 24 2010