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

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

%S 0,0,6,40,125,323,647,1235,2074,3337,5057,7477,10436,14490,19436,

%T 25591,33015,42259,52849,65833,80528,97909,117905,141163,166651,

%U 196474,229796,267289,308712,355766,406488,464094,526402,595477,670963

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

%C See A210000 for a guide to related sequences.

%H Chai Wah Wu, <a href="/A210291/b210291.txt">Table of n, a(n) for n = 0..1000</a>

%t a = 0; b = n; z1 = 45;

%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, n], {n, 0, z1}] (* A210291 *)

%Y Cf. A210000.

%K nonn

%O 0,3

%A _Clark Kimberling_, Mar 20 2012