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A211140 Number of 2 X 2 matrices having all terms in {-n,...,0,...,n} and determinant n.

%I A211140 #21 Jul 19 2017 20:23:34
%S A211140 1,20,92,176,364,408,880,704,1420,1412,2088,1552,3760,2104,3808,4096,
%T A211140 5388,3400,7660,4208,9160,7392,8464,5952,15344,8428,11656,11584,16608,
%U A211140 9208,22752,10464,21132,16928,19192,17952
%N A211140 Number of 2 X 2 matrices having all terms in {-n,...,0,...,n} and determinant n.
%C A211140 For a guide to related sequences, see A210000.
%C A211140 Also the number of 2 X 2 matrices having all terms in {-n,...,0,...,n} and permanent n [because #(a,b,c,d) with a,b,c,d in {-n..n} and a*d-b*c=n equals #(a,b,c,d) with a,b,c,d in {-n..n} and a*d+b*c=n. (Replace d with -d)]. - _Alois P. Heinz_, Jun 26 2012
%H A211140 Chai Wah Wu, <a href="/A211140/b211140.txt">Table of n, a(n) for n = 0..3000</a>
%t A211140 a = -n; b = n; z1 = 35;
%t A211140 t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
%t A211140 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A211140 Table[c[n, n], {n, 0, z1}]  (* A211140 *)
%Y A211140 Cf. A210000.
%K A211140 nonn
%O A211140 0,2
%A A211140 _Clark Kimberling_, Apr 02 2012