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 A272663 #16 May 05 2025 07:54:47
%S A272663 1,2,9,68,1161,65348
%N A272663 Number of distinct characteristic polynomials of n X n matrices with elements {t, 1}, where t is an indeterminate.
%H A272663 Robert M. Corless, <a href="https://www.youtube.com/watch?v=qB1KZWU8g2U">Bohemian Eigenvalues</a>, Talk Presented at Computational Discovery in Mathematics (ACMES 2), University of Western Ontario, May 12 2016. Rotman Institute of Philosophy, Youtube video. (Talk based on joint work with Steven E. Thornton, Sonia Gupta, Jonathan Brino-Tarasoff, Venkat Balasubramanian.)
%e A272663 From _Robin Visser_, May 01 2025: (Start)
%e A272663 For n = 1, the a(1) = 2 possible characteristic polynomials are x - 1 and x - t.
%e A272663 For n = 2, the a(2) = 9 possible characteristic polynomials are x^2 - 2*x, x^2 - 2*t*x, x^2 - 2*t*x + t^2 - t, x^2 + (-t - 1)*x, x^2 + (-t - 1)*x - t^2 + t, x^2 - 2*x - t^2 + 1, x^2 - 2*t*x + t^2 - 1, x^2 - 2*x - t + 1, and x^2 + (-t - 1)*x + t - 1. (End)
%o A272663 (Sage)
%o A272663 import itertools
%o A272663 def a(n):
%o A272663 ans, t = set(), SR('t')
%o A272663 W = itertools.product([t, 1], repeat=n*n)
%o A272663 for w in W: ans.add(Matrix(SR, n, n, w).charpoly())
%o A272663 return len(ans) # _Robin Visser_, May 01 2025
%Y A272663 Six classes of matrices mentioned in Rob Corless's talk: A272658, A272659, A272660, A272661, A272662, A272663.
%K A272663 nonn,hard,more
%O A272663 0,2
%A A272663 _N. J. A. Sloane_, May 15 2016
%E A272663 a(0)=1 prepended by _Alois P. Heinz_, Sep 28 2023
%E A272663 a(5) from _Robin Visser_, May 04 2025