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Number of 2 X 2 matrices having all terms in {1,...,n} and determinant in [-n,n].
1

%I #6 Jan 14 2017 01:37:22

%S 1,14,57,150,309,574,921,1444,2091,2952,3919,5314,6709,8534,10603,

%T 13102,15593,18962,22133,26332,30569,35346,40097,46690,52553,59394,

%U 66603,75094,82833,93282,102181,113422,124411,136412,148613

%N Number of 2 X 2 matrices having all terms in {1,...,n} and determinant in [-n,n].

%C For a guide to related sequences, see A210000.

%t a = 1; b = n; z1 = 35;

%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, -n, m}]

%t Table[c1[n, n], {n, 1, z1}] (* A211069 *)

%Y Cf. A210000.

%K nonn

%O 1,2

%A _Clark Kimberling_, Mar 31 2012