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A209981 Number of singular 2 X 2 matrices having all elements in {-n,...,n}.

%I A209981 #15 May 05 2020 01:59:38
%S A209981 1,33,129,289,545,833,1313,1729,2369,3041,3905,4577,5857,6657,7905,
%T A209981 9345,10881,11937,13953,15137,17441,19521,21537,22977,26177,28257,
%U A209981 30657,33249,36577,38401,42721,44673,48257,51617,54785,58529,63905
%N A209981 Number of singular 2 X 2 matrices having all elements in {-n,...,n}.
%C A209981 See A210000 for a guide to related sequences.
%H A209981 Chai Wah Wu, <a href="/A209981/b209981.txt">Table of n, a(n) for n = 0..10000</a>
%F A209981 a(n) = 8*A134506(n) + (4*n + 1)^2. - _Andrew Howroyd_, May 04 2020
%e A209981 Among the 33 matrices counted by a(1) are these (in compact notation):
%e A209981 (-1,-1,-1,-1), (0,0,0,0), (1,-1,-1,1), (1,1,1,1).
%t A209981 a = -n; b = n; z1 = 40;
%t A209981 t[n_] := t[n] = Flatten[Table[w*z - x*y, {w, a, b}, {x, a, b}, {y, a, b}, {z, a, b}]]
%t A209981 c[n_, k_] := c[n, k] = Count[t[n], k]
%t A209981 Table[c[n, 0], {n, 0, z1}]  (* A209981 *)
%t A209981 Table[c[n, 1], {n, 0, z1}]  (* A209982 *)
%t A209981 %/4                         (* A206258 *)
%t A209981 2 %                         (* A209983 *)
%t A209981 Table[c[n, 2], {n, 0, z1}]  (* A209984 *)
%t A209981 %/4                         (* A209985 *)
%t A209981 Table[c[n, 3], {n, 0, z1}]  (* A209986 *)
%t A209981 %/8                         (* A209987 *)
%t A209981 Table[c[n, 4], {n, 0, z1}]  (* A209988 *)
%t A209981 %/4                         (* A209989 *)
%t A209981 Table[c[n, 5], {n, 0, z1}]  (* A209990 *)
%t A209981 %/8                         (* A209997 *)
%Y A209981 Cf. A210000.
%K A209981 nonn
%O A209981 0,2
%A A209981 _Clark Kimberling_, Mar 17 2012