cp's OEIS Frontend

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

%I A279725 #52 May 04 2025 17:32:06
%S A279725 0,168,2022,15090,53160,196962,409956,1096368,2062140,4070796,6674010,
%T A279725 12603174,18410352,31642836,45306438,67301682,93747984,142196892,
%U A279725 183799392,267038772,342684960,458663640,582535842,793793994,963867732,1266864846,1550198598,1957887150,2357651670,3015489714
%N A279725 Number of 3 X 3 matrices having all terms in {0,1,...,n} with |det| = 1.
%C A279725 a(n) is always even.
%C A279725 a(n) mod 6 = 0.
%H A279725 Robin Visser, <a href="/A279725/b279725.txt">Table of n, a(n) for n = 0..35</a>
%H A279725 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/UnimodularMatrix.html">Unimodular Matrix</a>
%H A279725 Wikipedia, <a href="https://en.wikipedia.org/wiki/Unimodular_matrix">Unimodular Matrix</a>
%e A279725 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 A279725 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 A279725 So, for n=2, a(n)=2022.
%o A279725 (Sage)
%o A279725 import itertools
%o A279725 def a(n):
%o A279725     ans, W = 0, itertools.product(range(n+1), repeat=9)
%o A279725     for w in W:
%o A279725         if abs(Matrix(ZZ, 3, 3, w).det())==1: ans += 1
%o A279725     return ans  # _Robin Visser_, May 01 2025
%Y A279725 Cf. A210000.
%K A279725 nonn
%O A279725 0,2
%A A279725 _Indranil Ghosh_, Jan 04 2017
%E A279725 More terms from _Robin Visser_, May 01 2025