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A380287
Sum of the perimeters of the free polyominoes with n cells.
1
4, 6, 16, 48, 142, 472, 1670, 6364, 24604, 97668, 390070, 1570560, 6334644, 25617062, 103669288, 419930444, 1701635046, 6898183050
OFFSET
1,1
COMMENTS
The perimeters of any holes are included here.
FORMULA
a(n) = Sum_{k=2..n+1} 2*k*A342243(n,k). - Pontus von Brömssen, Jan 27 2025
EXAMPLE
Illustration for n = 4:
The free polyominoes with four cells are also called free tetrominoes.
The five free tetrominoes are as shown below:
_
|_| _ _ _
|_| |_| |_|_ |_|_ _ _
|_| |_|_ |_|_| |_|_| |_|_|
|_| |_|_| |_| |_| |_|_|
.
From left to right the perimeters are respectively [10, 10, 10, 10, 8] as shown below:
_
| | _ _ _
| | | | | |_ | |_ _ _
| | | |_ |_ | | _| | |
|_| |_ _| |_| |_| |_ _|
.
The sum of the perimeters is 10 + 10 + 10 + 10 + 8 = 48, so a(4) = 48.
.
CROSSREFS
See A380575 for another version.
Sequence in context: A072279 A038236 A223269 * A264471 A264477 A223357
KEYWORD
nonn,more,changed
AUTHOR
Omar E. Pol, Jan 25 2025
EXTENSIONS
a(6)-a(18) (using A342243 b-file) from Pontus von Brömssen, Jan 27 2025
STATUS
approved