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A211146 Number of 2 X 2 matrices having all terms in {-n,...,0,...,n} and 0 <= determinant <= n.

%I A211146 #10 Feb 02 2022 12:01:38
%S A211146 1,53,273,737,1613,2821,4853,7125,10593,14597,19885,25309,33677,41189,
%T A211146 51269,62565,76145,88793,106821,122581,144541,166045,189997,212877,
%U A211146 246653,275081,308369,343281,384977,421097,472649,513865,567765
%N A211146 Number of 2 X 2 matrices having all terms in {-n,...,0,...,n} and 0 <= determinant <= n.
%C A211146 For a guide to related sequences, see A210000.
%t A211146 a = -n; b = n; z1 = 35;
%t A211146 t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
%t A211146 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A211146 c1[n_, m_] := c1[n, m] = Sum[c[n, k], {k, 0, m}]
%t A211146 Table[c1[n, n], {n, 0, z1}]              (* A211146 *)
%t A211146 (1/4) (-1 + Table[c1[n, n], {n, 0, z1}]) (* integers *)
%Y A211146 Cf. A210000.
%K A211146 nonn
%O A211146 0,2
%A A211146 _Clark Kimberling_, Apr 03 2012
%E A211146 Offset changed to 0 by _Georg Fischer_, Feb 02 2022