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

0,2

Comments

See A210000 for a guide to related sequences.

Links

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

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)

Mathematica

(See the Mathematica section at A209981.)

Prog

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

Crossrefs

Cf. A171503, A196227, A210000.

Sequence in context: A350115 A211143 A183047 * A205220 A188250 A329627

Adjacent sequences: A209979 A209980 A209981 * A209983 A209984 A209985

Keyword

nonn

Author

Clark Kimberling, Mar 17 2012

Status

approved