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A309838 a(n) = number of dimensions of semisimple matrix subalgebras.

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%I A309838 #18 Sep 24 2019 21:41:10
%S A309838 2,4,7,11,16,22,29,39,50,60,73,88,103,120,139,160,181,203,229,256,284,
%T A309838 313,343,377,412,448,487,528,569,610,653,699,748,797,849,904,959,1014,
%U A309838 1070,1129,1191,1255,1321,1388,1456,1526,1598,1672,1746,1821,1899,1981,2064
%N A309838 a(n) = number of dimensions of semisimple matrix subalgebras.
%C A309838 a(n) = |A_n| in the Heikoop paper.
%C A309838 A semisimple matrix subalgebra of M_n(k) for an algebraically closed field k is a direct sum of M_n_i(k) such that Sum (n_i) <= n. See Heikoop paper, Section 3.2, for more.
%H A309838 Phillip Heikoop, <a href="/A309838/b309838.txt">Table of n, a(n) for n = 1..336</a>
%H A309838 Phillip Tomas Heikoop, <a href="https://digitalcommons.wpi.edu/mqp-all/6822">Dimensions of Matrix Subalgebras</a>, Bachelor's Thesis, Worcester Polytechnic Institute (2019).
%H A309838 Phillip Heikoop, <a href="/A309838/a309838.cpp.txt">C++11 code to generate the sequence</a>
%F A309838 a(n) <= n^2 - Sqrt(2) * Sqrt(2n+ 3) * n.
%Y A309838 Cf. A000124, A002620, A069999, A138544, A309839.
%K A309838 nonn
%O A309838 1,1
%A A309838 _Phillip Heikoop_, Aug 19 2019