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 A366551 #13 May 09 2025 17:13:26
%S A366551 1,32,513,4407,21393,86620,242057,673623,1467642,3107487,5836467,
%T A366551 11108595,18102935,31327359,48505904,74802671,110297111,166721570,
%U A366551 230270840
%N A366551 Number of distinct characteristic polynomials for 3 X 3 matrices with entries from {0, 1, ..., n}.
%H A366551 Robert P. P. McKone, <a href="/A366551/a366551_1.txt">The distinct characteristic polynomials for a(0)-a(6)</a>.
%F A366551 a(n) <= A366158(n) * A227776(n) * A016777(n).
%t A366551 mat[n_Integer?Positive] := mat[n] = Array[m, {n, n}]; flatMat[n_Integer?Positive] := flatMat[n] = Flatten[mat[n]]; charPolyMat[n_Integer?Positive] := charPolyMat[n] = FullSimplify[CoefficientList[Expand[CharacteristicPolynomial[mat[n], x]], x]]; a[d_Integer?Positive, 0] = 1; a[d_Integer?Positive, n_Integer?Positive] := a[d, n] = Length[DeleteDuplicates[Flatten[Table[Evaluate[charPolyMat[d]], ##] & @@ Table[{flatMat[d][[i]], 0, n}, {i, 1, d^2}], d^2 - 1]]]; Table[a[3, n], {n, 0, 7}]
%o A366551 (Sage)
%o A366551 import itertools
%o A366551 def a(n):
%o A366551 ans, W = set(), itertools.product(range(n+1), repeat=9)
%o A366551 for w in W: ans.add(Matrix(ZZ, 3, 3, w).charpoly())
%o A366551 return len(ans) # _Robin Visser_, May 08 2025
%Y A366551 Cf. A366448 (2 X 2 matrices), A367978 (4 X 4 matrices).
%Y A366551 Cf. A366158 (determinants), A227776 (2nd order coefficients), A016777 (traces).
%Y A366551 Cf. A272659.
%K A366551 nonn,more
%O A366551 0,2
%A A366551 _Robert P. P. McKone_, Oct 13 2023
%E A366551 a(12)-a(18) from _Robin Visser_, May 08 2025