A380287 Sum of the perimeters of the free polyominoes with n cells.
4, 6, 16, 48, 142, 472, 1670, 6364, 24604, 97668, 390070, 1570560, 6334644, 25617062, 103669288, 419930444, 1701635046, 6898183050
Offset: 1
Examples
Illustration for n = 4:
The free polyominoes with four cells are also called free tetrominoes.
The five free tetrominoes are as shown below:
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|_| _ _ _
|_| |_| |_|_ |_|_ _ _
|_| |_|_ |_|_| |_|_| |_|_|
|_| |_|_| |_| |_| |_|_|
.
From left to right the perimeters are respectively [10, 10, 10, 10, 8] as shown below:
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| | _ _ _
| | | | | |_ | |_ _ _
| | | |_ |_ | | _| | |
|_| |_ _| |_| |_| |_ _|
.
The sum of the perimeters is 10 + 10 + 10 + 10 + 8 = 48, so a(4) = 48.
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Crossrefs
Formula
a(n) = Sum_{k=2..n+1} 2*k*A342243(n,k). - Pontus von Brömssen, Jan 27 2025
Extensions
a(6)-a(18) (using A342243 b-file) from Pontus von Brömssen, Jan 27 2025
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