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A207259 The number of 2 X 2 matrices with no real eigenvalues and whose entries are integers of absolute value at most n. 2
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified January 27 13:45 EST 2022. Contains 350607 sequences. (Running on oeis4.)