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A210367 Number of 2 X 2 matrices with all elements in {0,1,...,n} and determinant >= 2n.

%I A210367 #13 Jul 22 2025 01:29:31
%S A210367 1,0,5,26,83,203,456,853,1497,2477,3860,5690,8305,11470,15684,20947,
%T A210367 27328,35057,44569,55569,68849,84153,101912,122125,146014,172246,
%U A210367 202378,236593,274399,316494,364473,416055,473938,537432,607225,683593,767218,857111,955830
%N A210367 Number of 2 X 2 matrices with all elements in {0,1,...,n} and determinant >= 2n.
%C A210367 See A210000 for a guide to related sequences.
%H A210367 Chai Wah Wu, <a href="/A210367/b210367.txt">Table of n, a(n) for n = 0..1000</a>
%e A210367 a(2)=5 counts these matrices:
%e A210367   2 0...2 1...2 0...2 0...2 2
%e A210367   0 2...0 2...1 2...2 2...0 2
%t A210367 a = 0; b = n; z1 = 20;
%t A210367 t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
%t A210367 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A210367 c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, 0, m}]
%t A210367 Table[c1[n, n^2] - c1[n, 2 n - 1], {n, 0, z1}]
%Y A210367 Cf. A210000.
%K A210367 nonn
%O A210367 0,3
%A A210367 _Clark Kimberling_, Mar 20 2012