A360915 - OEIS

A360915

Array read by antidiagonals: T(m,n) is the length of the longest induced cycle in the grid graph P_m X P_n.

4, 4, 4, 4, 8, 4, 4, 10, 10, 4, 4, 12, 12, 12, 4, 4, 14, 14, 14, 14, 4, 4, 16, 16, 16, 16, 16, 4, 4, 18, 20, 18, 18, 20, 18, 4, 4, 20, 22, 24, 20, 24, 22, 20, 4, 4, 22, 24, 26, 28, 28, 26, 24, 22, 4, 4, 24, 28, 28, 30, 32, 30, 28, 28, 24, 4, 4, 26, 30, 32, 32, 36, 36, 32, 32, 30, 26, 4

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OFFSET

2,1

COMMENTS

All terms are even since the grid graph is bipartite.

LINKS

Table of n, a(n) for n=2..79.

Nikolai Beluhov, Snake paths in king and knight graphs, arXiv:2301.01152 [math.CO], 2023.

Eric Weisstein's World of Mathematics, Grid Graph.

FORMULA

T(m,n) = T(n,m).

T(m,n) = 2*m*n/3 + O(m+n) (Beluhov 2023, Proposition 3). - Pontus von Brömssen, May 08 2023

EXAMPLE

Array begins:

==========================================

m\n| 2 3 4 5 6 7 8 9 10 11 12 ...

-----+------------------------------------

2 | 4 4 4 4 4 4 4 4 4 4 4 ...

3 | 4 8 10 12 14 16 18 20 22 24 26 ...

4 | 4 10 12 14 16 20 22 24 28 30 32 ...

5 | 4 12 14 16 18 24 26 28 32 36 38 ...

6 | 4 14 16 18 20 28 30 32 36 42 44 ...

7 | 4 16 20 24 28 32 36 40 44 48 52 ...

8 | 4 18 22 26 30 36 40 46 50 56 60 ...

9 | 4 20 24 28 32 40 46 50 56 62 68 ...

10 | 4 22 28 32 36 44 50 56 62 70 74 ...

11 | 4 24 30 36 42 48 56 62 70 76 82 ...

12 | 4 26 32 38 44 52 60 68 74 82 90 ...

...

CROSSREFS

Main diagonal is A357357.

Cf. A360196, A360913, A360917, A360920.

Sequence in context: A159835 A240835 A047210 * A120327 A056629 A245356

Adjacent sequences: A360912 A360913 A360914 * A360916 A360917 A360918

KEYWORD

nonn,tabl

AUTHOR

Andrew Howroyd, Feb 26 2023

STATUS

approved