login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
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. 4
1, 3, 5, 7, 17, 23, 31, 39, 51, 63, 75, 89, 105, 121, 139, 159 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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).
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?
LINKS
FORMULA
a(n) ~ 2*n^2/3. - Pontus von Brömssen, Sep 19 2022
a(n) <= A331968(n). - Pontus von Brömssen, Sep 21 2022
EXAMPLE
Longest snakes for 5 <= 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
CROSSREFS
Sequence in context: A137258 A053341 A331894 * A086086 A141772 A220454
KEYWORD
nonn,hard,more
AUTHOR
Yi Yang, Sep 18 2022
EXTENSIONS
a(1)-a(9) confirmed by Pontus von Brömssen, Sep 21 2022. - N. J. A. Sloane, Sep 30 2022
a(10)-a(13) confirmed by Elijah Beregovsky, Nov 27 2022
a(14)-a(16) from Andrew Howroyd, Feb 28 2023
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified March 1 02:07 EST 2024. Contains 370429 sequences. (Running on oeis4.)