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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
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
Sequence in context: A344378 A032468 A327286 * A359209 A182807 A306098
KEYWORD
nonn
AUTHOR
Nathaniel Johnston, Aug 27 2012
STATUS
approved

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Last modified May 23 22:02 EDT 2024. Contains 372765 sequences. (Running on oeis4.)