OFFSET
1,1
COMMENTS
A diagonalizable matrix A is one which can be expressed as XDY, where D is a diagonal matrix and X = Y^-1 are square matrices. By 'diagonalizable over C,' it is meant that the matrix D has complex entries.
The nondiagonalizable 2 x 2 matrices are the nondiagonal ones whose characteristic polynomial has discriminant 0. - Robert Israel, Nov 12 2020
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
Wikipedia, Diagonalizable matrix
MAPLE
N:= 30: # for a(1)..a(N)
V:= Vector(N):
for t from 1 to N do
for d in select(`<=`, numtheory:-divisors(t^2), N) do
for n from max(d, t^2/d) to N do
V[n]:= V[n] + (8*(n-t)+4)
od od od:
for n from 1 to N do V[n]:= (2*n+1)^4 - (V[n] + 4*n*(2*n+1)) od:
convert(V, list); # Robert Israel, Nov 12 2020
MATHEMATICA
a[n_] := Length[Select[Tuples[Tuples[Range[-n, n], 2], 2], DiagonalizableMatrixQ]];
CROSSREFS
KEYWORD
nonn
AUTHOR
Matthew Niemiro, Nov 07 2020
EXTENSIONS
More terms from Robert Israel, Nov 12 2020
STATUS
approved