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Search: id:A115077
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| A115077 |
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Number of 2 X 2 symmetric matrices over Z(n) having nonzero determinant. |
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+0
3
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| 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; listen)
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OFFSET
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1,2
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FORMULA
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a(n)=n^3-A115075(n). For squarefree n, a(n)=(n-1)n^2.
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MATHEMATICA
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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}]
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CROSSREFS
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Cf. A005353 (number of 2 X 2 matrices over Z(n) having nonzero determinant).
Sequence in context: A062235 A126283 A023618 this_sequence A066153 A023650 A045991
Adjacent sequences: A115074 A115075 A115076 this_sequence A115078 A115079 A115080
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KEYWORD
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nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jan 12 2006
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