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 A353071 #16 May 13 2022 18:13:34 %S A353071 1,4,9,7,15,36,49,64,37,100,65,144,169,123,225,124,199,324,197,400, %T A353071 441,484 %N A353071 Maximum number of clicks needed to solve any solvable Lights Out problem on an n X n grid. %C A353071 a(n) = n^2 if and only if A159257(n) = 0. %C A353071 a(n) >= A075464(n). %C A353071 If n = 6k-1 for some integer k, then a(n) <= 26k^2 - 12k + 1. This upper bound is equal to a(n) when A159257(n) = 2. Further, it is conjectured that if A159257(n) = 2, then n = 6k-1 for some integer k. %C A353071 It is conjectured that if A159257(n) = 4, then n = 5k-1 for some integer k, and a(n) = 17k^2 - 10k. %C A353071 It is conjectured that if A159257(n) = 6, then n = 12k-1 for some integer k, and a(n) = 88k^2 - 24k + 1 %C A353071 It is conjectured that if A159257(n) = 8, then either n = 10k-1 or n = 17k-1 for some integer k. If n = 10k-1, then a(n) = 60k^2 - 20k - 3. If n = 17k-1, then a(n) = 161k^2 - 34k - 3. %C A353071 It is conjectured that if A159257(n) = 10, then n = 30k-1 for some integer k, and a(n) = 506k^2 - 60k - 3. %C A353071 239 <= a(23) <= 305. %H A353071 William Boyles, <a href="https://arxiv.org/abs/2201.03452">Most Clicks Problem in Lights Out</a>, arXiv:2201.03452 [math.CO], 2022. %Y A353071 Cf. A159257, A075464. %K A353071 nonn,more,hard %O A353071 1,2 %A A353071 _William Boyles_, Apr 21 2022