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Number of 2 X 2 matrices with all elements in {0,1,...,n} and permanent = (trace)^2.
3

%I #9 Dec 14 2016 08:35:03

%S 1,5,9,15,25,29,35,53,63,81,85,89,107,141,159,165,193,197,215,261,271,

%T 323,327,331,349,389,423,461,529,533,539,617,645,651,655,673,727,817,

%U 863,959,969,973,1025,1131,1141,1159

%N Number of 2 X 2 matrices with all elements in {0,1,...,n} and permanent = (trace)^2.

%C See A210000 for a guide to related sequences.

%H Chai Wah Wu, <a href="/A210289/b210289.txt">Table of n, a(n) for n = 0..10000</a>

%t a = 0; b = n; z1 = 45;

%t t[n_] := t[n] = Flatten[Table[w^2 + z^2 + 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 Table[c[n, 0], {n, 0, z1}] (* A210289 *)

%Y Cf. A210000.

%K nonn

%O 0,2

%A _Clark Kimberling_, Mar 19 2012