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A272660 Number of distinct characteristic polynomials of n X n matrices with elements {t, 1, 2} where t is an indeterminate.

%I A272660 #11 May 04 2025 17:32:40
%S A272660 1,3,36,1782,760678
%N A272660 Number of distinct characteristic polynomials of n X n matrices with elements {t, 1, 2} where t is an indeterminate.
%D A272660 Robert M. Corless, Bohemian Eigenvalues, Talk Presented at Computational Discovery in Mathematics (ACMES 2), University of Western Ontario, May 12 2016. (Talk based on joint work with Steven E. Thornton, Sonia Gupta, Jonathan Brino-Tarasoff, Venkat Balasubramanian.)
%e A272660 From _Robin Visser_, May 01 2025: (Start)
%e A272660 For n = 1, the a(1) = 3 possible characteristic polynomials are x - 2, x - 1, and x - t.
%e A272660 For n = 2, the a(2) = 36 possible characteristic polynomials are x^2 - 2x - 1, x^2 - 2x, x^2 + (-t-2)x, x^2 + (-t-2)x - t^2+2t, x^2 + (-t-1)x, x^2 + (-t-1)x - t^2+t, x^2 - 4x, x^2 - 4x + 2, x^2 - 4x + 3, x^2 - 3x - 2, x^2 - 3x, x^2 - 3x + 1, x^2 - 2tx + t^2-4, x^2 - 2tx + t^2-2, x^2 - 2tx + t^2-1, x^2 + (-t-2)x + t, x^2 - 4x - t+4, x^2 - 4x - t^2+4, x^2 - 2x - 3, x^2 - 2tx, x^2 - 2tx + t^2-t, x^2 - 2tx + t^2-2t, x^2 - 4x - 2t+4, x^2 - 3x - t^2+2, x^2 - 3x - t+2, x^2 - 3x - 2t+2, x^2 - 2x - t^2+1, x^2 - 2x - t+1, x^2 - 2x - 2t+1, x^2 + (-t-2)x + 2t-4, x^2 + (-t-2)x + 2t-2, x^2 + (-t-2)x + 2t-1, x^2 + (-t-1)x + t-4, x^2 + (-t-1)x + t-2, x^2 + (-t-1)x + t-1, and x^2 + (-t-1)x - t. (End)
%o A272660 (Sage)
%o A272660 import itertools
%o A272660 def a(n):
%o A272660     ans, t = set(), SR('t')
%o A272660     W = itertools.product([t, 1, 2], repeat=n*n)
%o A272660     for w in W: ans.add(Matrix(SR, n, n, w).charpoly())
%o A272660     return len(ans)  # _Robin Visser_, May 01 2025
%Y A272660 Six classes of matrices mentioned in Rob Corless's talk: A272658, A272659, A272660, A272661, A272662, A272663.
%K A272660 nonn,more
%O A272660 0,2
%A A272660 _N. J. A. Sloane_, May 15 2016
%E A272660 a(0)=1 prepended by _Alois P. Heinz_, Sep 28 2023
%E A272660 a(4) from _Robin Visser_, May 01 2025