cp's OEIS Frontend

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

%I A207259 #44 Nov 21 2016 04:23:39
%S A207259 14,148,642,1832,4246,8420,15202,25296,39742,59668,86338,120840,
%T A207259 165174,220356,288322,370816,470254,587940,726994,888728,1076422,
%U A207259 1292404,1539442,1819440,2136734,2493700,2893586,3339544,3835782,4384036,4990466,5656752,6388158
%N A207259 The number of 2 X 2 matrices with no real eigenvalues and whose entries are integers of absolute value at most n.
%H A207259 Hiroaki Yamanouchi and Chai Wah Wu, <a href="/A207259/b207259.txt">Table of n, a(n) for n = 1..1000</a> (terms for n = 1..100 from Hiroaki Yamanouchi)
%F A207259 a(n) = (2*n+1)^4 - A219736(n).
%p A207259 a:=proc(n)
%p A207259 local x,y,z,w,Eig,count;
%p A207259 count:=0;
%p A207259 for x from -n to n do
%p A207259 for y from -n to n do
%p A207259 for z from -n to n do
%p A207259 for w from -n to n do
%p A207259 Eig:=LinearAlgebra:-Eigenvalues(Matrix([[x,y],[z,w]]));
%p A207259 if Im(Eig[1]) <> 0  then count:=count+1; fi;
%p A207259 od:
%p A207259 od:
%p A207259 od:
%p A207259 od:
%p A207259 count;
%p A207259 end:
%Y A207259 Cf. A003024, A219736, A219744.
%K A207259 nonn,easy
%O A207259 1,1
%A A207259 _W. Edwin Clark_, Nov 26 2012
%E A207259 a(16)-a(33) from _Hiroaki Yamanouchi_, Oct 03 2014