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A020478
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Number of singular 2 X 2 matrices over Z(n) (i.e. with determinant = 0).
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4
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1, 10, 33, 88, 145, 330, 385, 736, 945, 1450, 1441, 2904, 2353, 3850, 4785, 6016, 5185, 9450, 7201, 12760, 12705, 14410, 12673, 24288, 18625, 23530, 26001, 33880, 25201, 47850, 30721, 48640, 47553, 51850, 55825, 83160, 51985, 72010, 77649, 106720
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| T. D. Noe, Table of n, a(n) for n=1..1000
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FORMULA
| a(n) = n^4 - A005353(n). Multiplicative with a(p^e) = p^(2*e-1)*(p^(e+1)+p^e-1). - Vladeta Jovovic (vladeta(AT)eunet.rs), Apr 22 2002
Dirichlet g.f.: zeta(s-2)*zeta(s-3)/zeta(s-1).
A102631(n) | a(n).- R. J. Mathar, Mar 30 2011
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PROG
| (PARI) a(n)=if(n<1, 0, direuler(p=2, n, (1-p*X)/((1-p^2*X)*(1-p^3*X)))[n])
(PARI) a(n)=local(c=0); forvec(x=vector(4, k, [1, n]), c+=((x[1]*x[2]-x[3]*x[4])%n==0)); c
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CROSSREFS
| Cf. A059306, A062801.
Sequence in context: A081437 A162433 A003012 * A094170 A004638 A020479
Adjacent sequences: A020475 A020476 A020477 * A020479 A020480 A020481
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KEYWORD
| nonn,mult
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AUTHOR
| David W. Wilson (davidwwilson(AT)comcast.net)
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