A207259 The number of 2 X 2 matrices with no real eigenvalues and whose entries are integers of absolute value at most n.

14, 148, 642, 1832, 4246, 8420, 15202, 25296, 39742, 59668, 86338, 120840, 165174, 220356, 288322, 370816, 470254, 587940, 726994, 888728, 1076422, 1292404, 1539442, 1819440, 2136734, 2493700, 2893586, 3339544, 3835782, 4384036, 4990466, 5656752, 6388158

Offset

1,1

Links

Hiroaki Yamanouchi and Chai Wah Wu, Table of n, a(n) for n = 1..1000 (terms for n = 1..100 from Hiroaki Yamanouchi)

Formula

a(n) = (2*n+1)^4 - A219736(n).

Maple

a:=proc(n)
local x, y, z, w, Eig, count;
count:=0;
for x from -n to n do
for y from -n to n do
for z from -n to n do
for w from -n to n do
Eig:=LinearAlgebra:-Eigenvalues(Matrix([[x, y], [z, w]]));
if Im(Eig[1]) <> 0  then count:=count+1; fi;
od:
od:
od:
od:
count;
end:

Crossrefs

Cf. A003024, A219736, A219744.

Sequence in context: A027473 A002451 A302994 * A016170 A081201 A065899

Adjacent sequences: A207256 A207257 A207258 * A207260 A207261 A207262

Keyword

nonn,easy

Author

W. Edwin Clark, Nov 26 2012

Extensions

a(16)-a(33) from Hiroaki Yamanouchi, Oct 03 2014

Status

approved