A211146 - OEIS

%I #10 Feb 02 2022 12:01:38

%S 1,53,273,737,1613,2821,4853,7125,10593,14597,19885,25309,33677,41189,

%T 51269,62565,76145,88793,106821,122581,144541,166045,189997,212877,

%U 246653,275081,308369,343281,384977,421097,472649,513865,567765

%N Number of 2 X 2 matrices having all terms in {-n,...,0,...,n} and 0 <= determinant <= n.

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

%t a = -n; 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, 0, m}]

%t Table[c1[n, n], {n, 0, z1}]              (* A211146 *)

%t (1/4) (-1 + Table[c1[n, n], {n, 0, z1}]) (* integers *)

%Y Cf. A210000.

%K nonn

%O 0,2

%A _Clark Kimberling_, Apr 03 2012

%E Offset changed to 0 by _Georg Fischer_, Feb 02 2022