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

%I #7 Nov 29 2016 20:57:29

%S 1,0,5,26,83,203,456,853,1497,2477,3860,5690,8305,11470,15684,20947,

%T 27328,35057,44569,55569,68849

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

%C See A210000 for a guide to related sequences.

%H Chai Wah Wu, <a href="/A210367/b210367.txt">Table of n, a(n) for n = 0..1000</a>

%e a(2)=5 counts these matrices:

%e 2 0...2 1...2 0...2 0...2 2

%e 0 2...0 2...1 2...2 2...0 2

%t a = 0; b = n; z1 = 20;

%t t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]

%t c[n_, k_] := c[n, k] = Count[t[n], k]

%t c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, 0, m}]

%t Table[c1[n, n^2] - c1[n, 2 n - 1], {n, 0, z1}]

%Y Cf. A210000.

%K nonn

%O 0,3

%A _Clark Kimberling_, Mar 20 2012