A206258 1/8 the number of 2 X 2 -n..n arrays with a 2 X 2 -n..n inverse, i.e., with determinant +-1.

5, 13, 29, 45, 77, 93, 141, 173, 221, 253, 333, 365, 461, 509, 573, 637, 765, 813, 957, 1021, 1117, 1197, 1373, 1437, 1597, 1693, 1837, 1933, 2157, 2221, 2461, 2589, 2749, 2877, 3069, 3165, 3453, 3597, 3789, 3917, 4237, 4333, 4669, 4829, 5021, 5197, 5565

Offset: 1

Author

R. H. Hardin with Max Alekseyev, Feb 05 2012

Keywords

• nonn

Links

• R. H. Hardin, Table of n, a(n) for n = 1..334
• R. H. Hardin and Max Alekseyev, 2X2 -n..n with inverse in -n..n and totient function?, Seqfan list Feb 2012.

Crossrefs

Cf. A000010, A002088.

Programs

Mathematica

8* Accumulate[EulerPhi[Range[50]]] - 3 (* Amiram Eldar, Dec 13 2024 *)

Formula

a(n) = a(n-1) + 8*A000010(n).

From Amiram Eldar, Dec 13 2024: (Start)

a(n) = 8*A002088(n) - 3.

a(n) = (24/Pi^2) * n^2 + O(n*log(n)). (End)