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A215925 The number of distinct (up to unitary similarity) *-subalgebras of the n X n complex matrices. 2
1, 2, 5, 10, 21, 38, 72, 124, 218, 363, 607, 977, 1580, 2479, 3889, 5976, 9162, 13812, 20771, 30811, 45561, 66638, 97117, 140237, 201811, 288119, 409904, 579240, 815715, 1141916, 1593318, 2211453, 3059662, 4213395, 5784458, 7907783, 10779202, 14636771, 19819770 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A *-subalgebra is a subalgebra (i.e., a subspace closed under matrix multiplication) that is closed under the conjugate transpose operation.

Also the partial sums of A006171.

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 0..1000

EXAMPLE

There are 10 different (up to unitary similarity) *-subalgebras of the 3 X 3 complex matrices, which contain matrices of the following forms:

0 0 0 ... a 0 0 ... a 0 0 ... a 0 0 ... a b 0

0 0 0 ... 0 0 0 ... 0 a 0 ... 0 b 0 ... c d 0

0 0 0 ... 0 0 0 ... 0 0 0 ... 0 0 0 ... 0 0 0

. . . ... . . . ... . . . ... . . . ... . . .

a 0 0 ... a 0 0 ... a 0 0 ... a b 0 ... a b c

0 a 0 ... 0 b 0 ... 0 b 0 ... c d 0 ... d e f

0 0 a ... 0 0 b ... 0 0 c ... 0 0 e ... g h i

Thus a(3) = 10.

CROSSREFS

Cf. A215905, A215909, A215914.

Sequence in context: A262408 A032468 A327286 * A182807 A306098 A056599

Adjacent sequences:  A215922 A215923 A215924 * A215926 A215927 A215928

KEYWORD

nonn

AUTHOR

Nathaniel Johnston, Aug 27 2012

STATUS

approved

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Last modified October 13 20:38 EDT 2019. Contains 327981 sequences. (Running on oeis4.)