A279725 - OEIS

%I #46 Mar 08 2023 05:25:25

%S 0,168,2022,15090,53160,196962,409956,1096368,2062140,4070796,6674010,

%T 12603174,18410352,31642836,45306438

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

%C a(n) is always even.

%C a(n) mod 6 = 0.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/UnimodularMatrix.html">Unimodular Matrix</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Unimodular_matrix">Unimodular Matrix</a>

%e 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.

%e 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].

%e So, for n=2, a(n)=2022.

%Y Cf. A210000.

%K nonn,more

%O 0,2

%A _Indranil Ghosh_, Jan 04 2017