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A115077 Number of 2 X 2 symmetric matrices over Z(n) having nonzero determinant. 2
0, 4, 18, 44, 100, 180, 294, 432, 630, 900, 1210, 1548, 2028, 2548, 3150, 3744, 4624, 5436, 6498, 7500, 8820, 10164, 11638, 13104, 14900, 16900, 18792, 20972, 23548, 26100, 28830, 31360, 34848, 38148, 41650, 44676, 49284, 53428, 57798, 62000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..40.

FORMULA

a(n)=n^3-A115075(n). For squarefree n, a(n)=(n-1)n^2.

MATHEMATICA

Table[cnt=0; Do[m={{a, b}, {b, c}}; If[Det[m, Modulus->n]>0, cnt++ ], {a, 0, n-1}, {b, 0, n-1}, {c, 0, n-1}]; cnt, {n, 50}]

CROSSREFS

Cf. A005353 (number of 2 X 2 matrices over Z(n) having nonzero determinant).

Sequence in context: A187297 A126283 A023618 * A278046 A258634 A280599

Adjacent sequences:  A115074 A115075 A115076 * A115078 A115079 A115080

KEYWORD

nonn

AUTHOR

T. D. Noe, Jan 12 2006

STATUS

approved

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Last modified August 5 19:40 EDT 2021. Contains 346488 sequences. (Running on oeis4.)