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

6, 8, 15, 20, 28, 40, 48, 58, 73, 88, 104, 126

Offset

3,1

Comments

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.

Links

Table of n, a(n) for n=3..14.

Wikipedia, Induced path.

Formula

a(n) ~ 2*n^2/3.

a(n) <= A357359(n) + 1.

Example

Longest induced cycles for 3 <= n <= 8:
  X . X   X . . X   X . X . X   X X X . . .   X . X . X . X   X . X . X X . X
  X X .   X X . .   X . X X .   X . X X X .   X . X . X X .   X . X X . X X .
  . X X   . X X .   X X . X .   X X . . X .   X . X X . X .   X X . X X . X .
          . . X X   . X . X X   . X . . X X   X X . X . X .   . X X . X . X X
                    . X X . X   . X X X . X   . X . X . X X   X . X . X X . X
                                . . . X X X   . X . X X . X   X . X X . X X .
                                              . X X . X . X   X X . X X . X .
                                                              . X X . X . X X

Crossrefs

Cf. A000937, A297669, A357357, A357359.

Sequence in context: A100914 A076672 A315924 * A315925 A315926 A063534

Adjacent sequences: A357355 A357356 A357357 * A357359 A357360 A357361

Keyword

nonn,more

Author

Pontus von Brömssen, Sep 25 2022

Extensions

a(9)-a(12) from Elijah Beregovsky, Dec 11 2022

a(13)-a(14) from Elijah Beregovsky, Dec 13 2022

Status

approved