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 A357234 #48 Feb 28 2023 13:07:15 %S A357234 1,3,5,7,17,23,31,39,51,63,75,89,105,121,139,159 %N A357234 a(n) is the maximum length of a snake-like polyomino in an n X n square that starts and ends at opposite corners. %C A357234 Snake-like polyominoes have all cells with at most two neighbor cells, and have at least one cell that has only one neighbor cell, where neighbors are horizontal or vertical (not diagonal). %C A357234 Lower bounds for a(10)-a(22) are 63, 75, 89, 105, 121, 139, 159, 179, 201, 225, 249, 275, 303. Is it true that a(n) = round((2*n*n-4*n+28)/3) for n >= 9? %H A357234 Yi Yang, <a href="/A357234/a357234.png">The longest snakes presently known that start and end at opposite corners in the n X n square up to n = 17</a>. %H A357234 Yi Yang, <a href="https://tieba.baidu.com/p/8049203368">A post that shows the lower bounds for a(18)-a(22)</a>. %H A357234 Yi Yang, <a href="https://bbs.emath.ac.cn/thread-18542-4-1.html">A C++ program that generates upper bounds for a(n) up to n = 19</a>. %F A357234 a(n) ~ 2*n^2/3. - _Pontus von Brömssen_, Sep 19 2022 %F A357234 a(n) <= A331968(n). - _Pontus von Brömssen_, Sep 21 2022 %e A357234 Longest snakes for 5 <= n <= 8: %e A357234 X X X X X X X X X X X X X X . X X X X . X X X X X X %e A357234 . . . . X . . . . . X . . X . X . X X . X . . . . X %e A357234 X X X X X X X X X X X X X X . X . X X . X X X X . X %e A357234 X . . . . X . . . . . X . . X X . X X X . . . X . X %e A357234 X X X X X X . X X X X X . . X . X X . X . X X X . X %e A357234 X X X . . X X . . X . X . X X . X . . X X %e A357234 X X X X . X X X . . X . . X . %e A357234 X X X X . . X X %Y A357234 Cf. A331968, A357516. %K A357234 nonn,hard,more %O A357234 1,2 %A A357234 _Yi Yang_, Sep 18 2022 %E A357234 a(1)-a(9) confirmed by _Pontus von Brömssen_, Sep 21 2022. - _N. J. A. Sloane_, Sep 30 2022 %E A357234 a(10)-a(13) confirmed by _Elijah Beregovsky_, Nov 27 2022 %E A357234 a(14)-a(16) from _Andrew Howroyd_, Feb 28 2023