The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
The OEIS is supported by the many generous donors to the OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 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: A344378 A032468 A327286 * A359209 A182807 A306098 Adjacent sequences: A215922 A215923 A215924 * A215926 A215927 A215928 KEYWORD nonn AUTHOR Nathaniel Johnston, Aug 27 2012 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

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