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%I #6 Dec 15 2016 01:21:52
%S 1,2,5,10,21,38,72,124,218,363,607,977,1580,2479,3889,5976,9162,13812,
%T 20771,30811,45561,66638,97117,140237,201811,288119,409904,579240,
%U 815715,1141916,1593318,2211453,3059662,4213395,5784458,7907783,10779202,14636771,19819770
%N The number of distinct (up to unitary similarity) *-subalgebras of the n X n complex matrices.
%C A *-subalgebra is a subalgebra (i.e., a subspace closed under matrix multiplication) that is closed under the conjugate transpose operation.
%C Also the partial sums of A006171.
%H Nathaniel Johnston, <a href="/A215925/b215925.txt">Table of n, a(n) for n = 0..1000</a>
%e There are 10 different (up to unitary similarity) *-subalgebras of the 3 X 3 complex matrices, which contain matrices of the following forms:
%e 0 0 0 ... a 0 0 ... a 0 0 ... a 0 0 ... a b 0
%e 0 0 0 ... 0 0 0 ... 0 a 0 ... 0 b 0 ... c d 0
%e 0 0 0 ... 0 0 0 ... 0 0 0 ... 0 0 0 ... 0 0 0
%e . . . ... . . . ... . . . ... . . . ... . . .
%e a 0 0 ... a 0 0 ... a 0 0 ... a b 0 ... a b c
%e 0 a 0 ... 0 b 0 ... 0 b 0 ... c d 0 ... d e f
%e 0 0 a ... 0 0 b ... 0 0 c ... 0 0 e ... g h i
%e Thus a(3) = 10.
%Y Cf. A215905, A215909, A215914.
%K nonn
%O 0,2
%A _Nathaniel Johnston_, Aug 27 2012
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