OFFSET
1,2
COMMENTS
Equivalently, T(m,n) is the maximum number of unit squares of a snake-like polyomino in an m X n rectangle.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 1..435
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| 1 2 3 4 5 6 7 8 9 10 11 12 ...
-----+----------------------------------------
1 | 1 2 3 4 5 6 7 8 9 10 11 12 ...
2 | 2 3 5 6 8 9 11 12 14 15 17 18 ...
3 | 3 5 7 9 11 14 16 18 20 22 24 26 ...
4 | 4 6 9 11 14 17 20 22 25 28 30 33 ...
5 | 5 8 11 14 17 21 24 27 30 34 37 40 ...
6 | 6 9 14 17 21 24 29 32 36 40 44 47 ...
7 | 7 11 16 20 24 29 33 38 42 46 50 55 ...
8 | 8 12 18 22 27 32 38 42 48 52 57 62 ...
9 | 9 14 20 25 30 36 42 48 53 58 64 70 ...
10 | 10 15 22 28 34 40 46 52 58 64 71 77 ...
11 | 11 17 24 30 37 44 50 57 64 71 77 86 ...
12 | 12 18 26 33 40 47 55 62 70 77 86 92 ...
...
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Andrew Howroyd, Feb 26 2023
STATUS
approved