cp's OEIS Frontend

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.

A357358 Length of the longest induced cycle in the n X n torus grid graph.

This page as a plain text file.
%I A357358 #18 Dec 14 2022 09:49:45
%S A357358 6,8,15,20,28,40,48,58,73,88,104,126
%N A357358 Length of the longest induced cycle in the n X n torus grid graph.
%C A357358 It is somewhat unclear how a(2) should be defined. If the 2 X 2 torus grid graph is considered to have multiple edges we have a(2) = 2 (a double edge between two nodes makes a 2-cycle), otherwise a(2) = 4.
%H A357358 Wikipedia, <a href="https://en.wikipedia.org/wiki/Induced_path">Induced path</a>.
%F A357358 a(n) ~ 2*n^2/3.
%F A357358 a(n) <= A357359(n) + 1.
%e A357358 Longest induced cycles for 3 <= n <= 8:
%e A357358   X . X   X . . X   X . X . X   X X X . . .   X . X . X . X   X . X . X X . X
%e A357358   X X .   X X . .   X . X X .   X . X X X .   X . X . X X .   X . X X . X X .
%e A357358   . X X   . X X .   X X . X .   X X . . X .   X . X X . X .   X X . X X . X .
%e A357358           . . X X   . X . X X   . X . . X X   X X . X . X .   . X X . X . X X
%e A357358                     . X X . X   . X X X . X   . X . X . X X   X . X . X X . X
%e A357358                                 . . . X X X   . X . X X . X   X . X X . X X .
%e A357358                                               . X X . X . X   X X . X X . X .
%e A357358                                                               . X X . X . X X
%Y A357358 Cf. A000937, A297669, A357357, A357359.
%K A357358 nonn,more
%O A357358 3,1
%A A357358 _Pontus von Brömssen_, Sep 25 2022
%E A357358 a(9)-a(12) from _Elijah Beregovsky_, Dec 11 2022
%E A357358 a(13)-a(14) from _Elijah Beregovsky_, Dec 13 2022