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%I #12 Dec 29 2024 10:56:34
%S 3,10,20,36,63,120
%N Number of positive roots in reflection group E_n.
%D J. E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge, 1990. See Table 3.2, page 80.
%H M. Golafshan, M. Rigo, and M. Whiteland, <a href="https://arxiv.org/abs/2412.18425">Computing the k-binomial complexity of generalized Thue-Morse words</a>, arXiv:2412.18425 [math.CO], 2024. See p. 29.
%e Starting with the Coxeter-Dynkin diagram for E_8, one repeatedly chops off nodes from one end, getting the sequence E_8, E_7, E_6, D_5, A_4, A_2 X A_1, for which the numbers of positive roots are 120, 63, 36, 20, 10, 3 X 1=3.
%Y Cf. A272696.
%K nonn,fini,full
%O 3,1
%A _N. J. A. Sloane_, May 05 2016