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A020478 Number of singular 2 X 2 matrices over Z(n) (i.e., with determinant = 0). 5
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; text; internal format)
OFFSET

1,2

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

FORMULA

a(n) = n^4 - A005353(n). Multiplicative with a(p^e) = p^(2*e - 1)*(p^(e+1) + p^e - 1). - Vladeta Jovovic, 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

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

CROSSREFS

Cf. A059306, A062801, A240547.

Sequence in context: A085490 A162433 A003012 * A094170 A004638 A211033

Adjacent sequences:  A020475 A020476 A020477 * A020479 A020480 A020481

KEYWORD

nonn,mult

AUTHOR

David W. Wilson

STATUS

approved

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Last modified January 23 00:56 EST 2019. Contains 319365 sequences. (Running on oeis4.)