A309838 a(n) = number of dimensions of semisimple matrix subalgebras.

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

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 * A334251 A175776 A177176

Adjacent sequences: A309835 A309836 A309837 * A309839 A309840 A309841

Keyword

nonn

Author

Phillip Heikoop, Aug 19 2019

Status

approved