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%I #3 Mar 30 2012 17:22:41
%S 1,36,261,1408,3225,9396,17101,47104,76545,116100,162261,367488,
%T 373321,615636,841725,1638400,1424481,2755620,2482597,4540800,4463361,
%U 5841396,6447981,12294144,11640625,13439556,18954729,24078208,20534697,30302100
%N Number of 3 X 3 symmetric matrices over Z(n) having determinant 0.
%F a(n)=n^6-A115225(n). For prime n, a(n)=(n^3+n-1)n^2.
%t Table[cnt=0; Do[m={{a, b, c}, {b, d, e}, {c, e, f}}; If[Det[m, Modulus->n]==0, cnt++ ], {a, 0, n-1}, {b, 0, n-1}, {c, 0, n-1}, {d, 0, n-1}, {e, 0, n-1}, {f, 0, n-1}]; cnt, {n, 2, 20}]
%Y Cf. A115221 (number of 3 X 3 matrices over Z(n) having determinant 0).
%K mult,nonn
%O 1,2
%A _T. D. Noe_, Jan 16 2006
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