This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A380287 #24 Mar 02 2025 23:19:14
%S A380287 4,6,16,48,142,472,1670,6364,24604,97668,390070,1570560,6334644,
%T A380287 25617062,103669288,419930444,1701635046,6898183050
%N A380287 Sum of the perimeters of the free polyominoes with n cells.
%C A380287 The perimeters of any holes are included here.
%H A380287 <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>.
%F A380287 a(n) = Sum_{k=2..n+1} 2*k*A342243(n,k). - _Pontus von Brömssen_, Jan 27 2025
%e A380287 Illustration for n = 4:
%e A380287 The free polyominoes with four cells are also called free tetrominoes.
%e A380287 The five free tetrominoes are as shown below:
%e A380287 _
%e A380287 |_| _ _ _
%e A380287 |_| |_| |_|_ |_|_ _ _
%e A380287 |_| |_|_ |_|_| |_|_| |_|_|
%e A380287 |_| |_|_| |_| |_| |_|_|
%e A380287 .
%e A380287 From left to right the perimeters are respectively [10, 10, 10, 10, 8] as shown below:
%e A380287 _
%e A380287 | | _ _ _
%e A380287 | | | | | |_ | |_ _ _
%e A380287 | | | |_ |_ | | _| | |
%e A380287 |_| |_ _| |_| |_| |_ _|
%e A380287 .
%e A380287 The sum of the perimeters is 10 + 10 + 10 + 10 + 8 = 48, so a(4) = 48.
%e A380287 .
%Y A380287 Cf. A000105, A027709, A057730, A130622, A131482, A135942, A342243.
%Y A380287 See A380575 for another version.
%K A380287 nonn,more
%O A380287 1,1
%A A380287 _Omar E. Pol_, Jan 25 2025
%E A380287 a(6)-a(18) (using A342243 b-file) from _Pontus von Brömssen_, Jan 27 2025