This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A366158 #46 Aug 27 2025 03:58:08
%S A366158 1,5,25,77,179,355,609,995,1497,2167,2999,4069,5289,6841,8595,10661,
%T A366158 13023,15777,18795,22305,26085,30397,35107,40381,45929,52247,58929,
%U A366158 66287,74139,82767,91643,101701,112013,123235
%N A366158 Number of distinct determinants of 3 X 3 matrices with entries from {0, 1, ..., n}.
%C A366158 These determinants a(n) equivalently represent the leading coefficient (coefficient of term with degree 0) of the characteristic polynomials for such matrices, thereby providing a direct measure and lower bound of the uniqueness of these polynomials within this matrix class.
%C A366158 The maximal determinant counted by a(n) is A033431(n) = 2*n^3.
%H A366158 Robert P. P. McKone, <a href="/A366158/a366158.txt">The distinct determinants for a(0)-a(18)</a>.
%t A366158 mat[n_Integer?Positive] := mat[n] = Array[m, {n, n}]; flatMat[n_Integer?Positive] := flatMat[n] = Flatten[mat[n]]; detMat[n_Integer?Positive] := detMat[n] = Det[mat[n]] // FullSimplify; a[d_Integer?Positive, 0] = 1; a[d_Integer?Positive, n_Integer?Positive] := a[d, n] = Length[DeleteDuplicates[Flatten[ParallelTable[Evaluate[detMat[d]], ##] & @@ Table[{flatMat[d][[i]], 0, n}, {i, 1, d^2}]]]]; Table[a[3, n], {n, 0, 9}]
%o A366158 (Python)
%o A366158 from itertools import product
%o A366158 def A366158(n): return len({a[0]*(a[4]*a[8] - a[5]*a[7]) - a[1]*(a[3]*a[8] - a[5]*a[6]) + a[2]*(a[3]*a[7] - a[4]*a[6]) for a in product(range(n+1),repeat=9)}) # _Chai Wah Wu_, Oct 06 2023
%Y A366158 Cf. A058331 (distinct determinants for 2 X 2 matrices).
%Y A366158 Cf. A272661, A272659.
%Y A366158 Cf. A365926.
%Y A366158 Cf. A272658, A272660, A272662, A272663.
%Y A366158 Cf. A033431 (maximal determinant).
%Y A366158 Cf. A097400 (distinct consecutive entries in 3 X 3 matrix).
%K A366158 nonn,more,changed
%O A366158 0,2
%A A366158 _Robert P. P. McKone_, Oct 02 2023
%E A366158 a(19)-a(26) from _Robin Visser_, May 08 2025
%E A366158 a(27)-a(33) from _Robin Visser_, Aug 26 2025