A209982 Number of 2 X 2 matrices having all elements in {-n,...,n} and determinant 1.

0, 20, 52, 116, 180, 308, 372, 564, 692, 884, 1012, 1332, 1460, 1844, 2036, 2292, 2548, 3060, 3252, 3828, 4084, 4468, 4788, 5492, 5748, 6388, 6772, 7348, 7732, 8628, 8884, 9844, 10356, 10996, 11508, 12276, 12660, 13812, 14388, 15156

Offset: 0

Author

Clark Kimberling, Mar 17 2012

Keywords

• nonn

Comments

See A210000 for a guide to related sequences.

Links

• Andrew Howroyd, Table of n, a(n) for n = 0..1000

Crossrefs

Cf. A171503, A196227, A210000.

Programs

Mathematica

(See the Mathematica section at A209981.)

PARI

a(n)=if(n<1, 0, 32*sum(k=1, n, eulerphi(k)) - 12) \\ Andrew Howroyd, May 05 2020

Formula

From Andrew Howroyd, May 05 2020: (Start)

a(n) = 8*A196227(n) + 4*(4*n + 1) = 8*A171503(n) - 4 for n > 0.

a(n) = -12 + 32*Sum_{k=1..n} phi(k) for n > 0. (End)