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

%I #6 Jan 12 2017 01:37:01

%S 0,1,8,23,46,77,120,167,230,301,384,463,590,685,808,959,1118,1245,

%T 1448,1591,1830,2053,2256,2431,2766,3005,3248,3535,3886,4109,4560,

%U 4799,5182,5549,5872,6295,6870,7157,7520,7959,8582

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

%C See A210000 for a guide to related sequences.

%t a = 1; b = n; z1 = 40;

%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, 1}]

%t Table[c1[n, 1], {n, 0, z1}] (* A209992 *)

%Y Cf. A210000.

%K nonn

%O 0,3

%A _Clark Kimberling_, Mar 18 2012