A279725 Number of 3 X 3 matrices having all terms in {0,1,...,n} with |det| = 1.

0, 168, 2022, 15090, 53160, 196962, 409956, 1096368, 2062140, 4070796, 6674010, 12603174, 18410352, 31642836, 45306438

Offset

0,2

Comments

a(n) is always even.

a(n) mod 6 = 0.

Links

Table of n, a(n) for n=0..14.

Eric Weisstein's World of Mathematics, Unimodular Matrix

Wikipedia, Unimodular Matrix

Example

For n=2, a few of the possible matrices are [0,0,1,0,1,0,1,0,0], [0,0,1,0,1,0,1,0,1], [0,0,1,0,1,0,1,0,2], [1,0,0,0,1,1,2,0,1], [1,0,0,0,1,1,2,1,0], [1,0,0,0,1,1,2,1,2], [2,2,1,2,1,2,1,0,2], [2,2,1,2,1,2,1,1,0], [2,2,1,2,1,2,1,1,1], [2,2,1,2,1,2,1,2,0], .... There are 2022 possibilities.
Here each of the matrices is defined as M=[a,b,c,d,e,f,g,h,i] where a=M[1][1], b=M[1][2], c=M[1][3], d=M[2][1], e=M[2][2], f=M[2][3], g=M[3][1], h=M[3][2] and i=M[3][3].
So, for n=2, a(n)=2022.

Crossrefs

Cf. A210000.

Sequence in context: A216107 A235932 A235926 * A234730 A234815 A232274

Adjacent sequences: A279722 A279723 A279724 * A279726 A279727 A279728

Keyword

nonn,more

Author

Indranil Ghosh, Jan 04 2017

Status

approved