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A115223
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Number of 3 X 3 symmetric matrices over Z(n) having determinant 0.
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1
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1, 36, 261, 1408, 3225, 9396, 17101, 47104, 76545, 116100, 162261, 367488, 373321, 615636, 841725, 1638400, 1424481, 2755620, 2482597, 4540800, 4463361, 5841396, 6447981, 12294144, 11640625, 13439556, 18954729, 24078208, 20534697, 30302100
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OFFSET
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1,2
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LINKS
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FORMULA
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a(n)=n^6-A115225(n). For prime n, a(n)=(n^3+n-1)n^2.
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A115221 (number of 3 X 3 matrices over Z(n) having determinant 0).
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KEYWORD
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mult,nonn
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AUTHOR
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STATUS
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approved
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