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Search: id:A115075
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| A115075 |
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Number of 2 X 2 symmetric matrices over Z(n) having determinant 0. |
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+0
3
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| 1, 4, 9, 20, 25, 36, 49, 80, 99, 100, 121, 180, 169, 196, 225, 352, 289, 396, 361, 500, 441, 484, 529, 720, 725, 676, 891, 980, 841, 900, 961, 1408, 1089, 1156, 1225, 1980, 1369, 1444, 1521, 2000, 1681, 1764, 1849, 2420, 2475, 2116, 2209, 3168, 2695, 2900
(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-A115077(n). For squarefree n, a(n)=n^2. Multiplicative with a(p^e)=p^(e)*(p^(e)+p^(e-1)-p^(ceiling(e/2)-1))
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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. A020478 (number of singular 2 X 2 matrices over Z(n)).
Sequence in context: A034479 A023377 A136769 this_sequence A063454 A053807 A066109
Adjacent sequences: A115072 A115073 A115074 this_sequence A115076 A115077 A115078
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KEYWORD
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mult,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Jan 12 2006
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