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 A368539 #30 Feb 03 2024 10:14:39
%S A368539 1,54,761,5284
%N A368539 Maximal sum of elements of A^2 where A is a square matrix of size n whose elements are a permutation of {1, 2, ..., n^2}.
%C A368539 The next terms are at least (and probably equal to) 5284, 24303, 85352 and 248045.
%C A368539 The lower bounds for the terms a(4)-a(7) are confirmed. a(8) >= 626610, a(9) >= 1421271, a(10) >= 2959798, a(11) >= 5750977. - _Hugo Pfoertner_, Jan 21 2024
%C A368539 In addition to the conditions (a)-(d) described in para 2.2 of Fried and Mansour (2023), conjecturally optimal matrices found using simulated annealing have the following additional property: If, using simultaneous row and column rearrangement, the matrix is brought into a form in which the terms of the main diagonal are sorted in ascending order, then every single row and every single column is monotonically increasing. See the linked file for examples from n=2 to n=14. - _Hugo Pfoertner_, Jan 25 2024
%H A368539 Sela Fried and Toufik Mansour, <a href="https://arxiv.org/abs/2308.00348">On the maximal sum of the entries of a matrix power</a>, arXiv:2308.00348 [math.CO], 2023.
%H A368539 Hugo Pfoertner, <a href="/A368539/a368539.txt">Examples of solutions found by simulated annealing</a>, for n=2-14. Jan 25, 2024.
%e A368539 [1 3 4]
%e A368539 For n = 3, the sum of the elements of A^2, where A = [2 6 8], is 761.
%e A368539 [5 7 9]
%Y A368539 Cf. A085000, A350566, A369396.
%K A368539 nonn,hard,more
%O A368539 1,2
%A A368539 _Sela Fried_, Dec 29 2023