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.
%I A215925 #10 Jul 26 2024 11:41:02 %S A215925 1,2,5,10,21,38,72,124,218,363,607,977,1580,2479,3889,5976,9162,13812, %T A215925 20771,30811,45561,66638,97117,140237,201811,288119,409904,579240, %U A215925 815715,1141916,1593318,2211453,3059662,4213395,5784458,7907783,10779202,14636771,19819770 %N A215925 The number of distinct (up to unitary similarity) *-subalgebras of the n X n complex matrices. %C A215925 A *-subalgebra is a subalgebra (i.e., a subspace closed under matrix multiplication) that is closed under the conjugate transpose operation. %C A215925 Also the partial sums of A006171. %H A215925 Nathaniel Johnston, <a href="/A215925/b215925.txt">Table of n, a(n) for n = 0..1000</a> %H A215925 William Q. Erickson, <a href="https://arxiv.org/abs/2407.13165">The Demazure product extended to biwords</a>, arXiv:2407.13165 [math.CO], 2024. See p. 16. %e A215925 There are 10 different (up to unitary similarity) *-subalgebras of the 3 X 3 complex matrices, which contain matrices of the following forms: %e A215925 0 0 0 ... a 0 0 ... a 0 0 ... a 0 0 ... a b 0 %e A215925 0 0 0 ... 0 0 0 ... 0 a 0 ... 0 b 0 ... c d 0 %e A215925 0 0 0 ... 0 0 0 ... 0 0 0 ... 0 0 0 ... 0 0 0 %e A215925 . . . ... . . . ... . . . ... . . . ... . . . %e A215925 a 0 0 ... a 0 0 ... a 0 0 ... a b 0 ... a b c %e A215925 0 a 0 ... 0 b 0 ... 0 b 0 ... c d 0 ... d e f %e A215925 0 0 a ... 0 0 b ... 0 0 c ... 0 0 e ... g h i %e A215925 Thus a(3) = 10. %Y A215925 Cf. A215905, A215909, A215914. %K A215925 nonn %O A215925 0,2 %A A215925 _Nathaniel Johnston_, Aug 27 2012