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A115223 Number of 3 X 3 symmetric matrices over Z(n) having determinant 0. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..30.

FORMULA

a(n)=n^6-A115225(n). For prime n, a(n)=(n^3+n-1)n^2.

MATHEMATICA

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}]

CROSSREFS

Cf. A115221 (number of 3 X 3 matrices over Z(n) having determinant 0).

Sequence in context: A017342 A115332 A133072 * A135181 A220159 A202958

Adjacent sequences:  A115220 A115221 A115222 * A115224 A115225 A115226

KEYWORD

mult,nonn

AUTHOR

T. D. Noe, Jan 16 2006

STATUS

approved

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Last modified May 22 14:32 EDT 2019. Contains 323480 sequences. (Running on oeis4.)