

A309838


a(n) = number of dimensions of semisimple matrix subalgebras.


2



2, 4, 7, 11, 16, 22, 29, 39, 50, 60, 73, 88, 103, 120, 139, 160, 181, 203, 229, 256, 284, 313, 343, 377, 412, 448, 487, 528, 569, 610, 653, 699, 748, 797, 849, 904, 959, 1014, 1070, 1129, 1191, 1255, 1321, 1388, 1456, 1526, 1598, 1672, 1746, 1821, 1899, 1981, 2064
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OFFSET

1,1


COMMENTS

a(n) = A_n in the Heikoop paper.
A semisimple matrix subalgebra of M_n(k) for an algebraically closed field k is a direct sum of M_n_i(k) such that Sum (n_i) <= n. See Heikoop paper, Section 3.2, for more.


LINKS

Phillip Heikoop, Table of n, a(n) for n = 1..336
Phillip Tomas Heikoop, Dimensions of Matrix Subalgebras, Bachelor's Thesis, Worcester Polytechnic Institute (2019).
Phillip Heikoop, C++11 code to generate the sequence


FORMULA

a(n) <= n^2  Sqrt(2) * Sqrt(2n+ 3) * n.


CROSSREFS

Cf. A000124, A002620, A069999, A138544, A309839.
Sequence in context: A175777 A098574 A212366 * A175776 A177176 A005689
Adjacent sequences: A309835 A309836 A309837 * A309839 A309840 A309841


KEYWORD

nonn


AUTHOR

Phillip Heikoop, Aug 19 2019


STATUS

approved



