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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. 3
 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 August 6 00:15 EDT 2024. Contains 374957 sequences. (Running on oeis4.)