A215925 The number of distinct (up to unitary similarity) *-subalgebras of the n X n complex matrices.

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

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: A344378 A032468 A327286 * A359209 A182807 A306098

Adjacent sequences: A215922 A215923 A215924 * A215926 A215927 A215928

Keyword

nonn

Author

Nathaniel Johnston, Aug 27 2012

Status

approved