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 A379628 #43 Feb 16 2025 13:55:05 %S A379628 0,0,1,6,35,143,631,2747,12027,52470,227993,985522,4235295,18114067, %T A379628 77112058,327000797,1381807943,5821692946 %N A379628 Total area between the free polyominoes with n cells and their bounding boxes. %C A379628 a(n) includes the area of any holes in the polyominoes. %H A379628 <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>. %F A379628 a(n) = A379627(n) - A057766(n). %e A379628 Illustration for n = 4: %e A379628 The free polyominoes with four cells are also called free tetrominoes. %e A379628 The five free tetrominoes are as shown below: %e A379628 _ %e A379628 |_| _ _ _ %e A379628 |_| |_| |_|_ |_|_ _ _ %e A379628 |_| |_|_ |_|_| |_|_| |_|_| %e A379628 |_| |_|_| |_| |_| |_|_| %e A379628 . %e A379628 The bounding boxes are respectively as shown below: %e A379628 _ %e A379628 | | _ _ _ _ _ _ %e A379628 | | | | | | | | _ _ %e A379628 | | | | | | | | | | %e A379628 |_| |_ _| |_ _| |_ _| |_ _| %e A379628 . %e A379628 4 x 1 3 X 2 3 X 2 3 X 2 2 X 2 %e A379628 . %e A379628 The total area of the free tetrominoes is 5*4 = 20. %e A379628 The total area of the bounding boxes is 4 + 6 + 6 + 6 + 4 = 26. %e A379628 The total area between the bounding boxes and the free tetrominoes is 26 - 20 = 6, so a(4) = 6. %e A379628 . %Y A379628 Cf. A000105, A057766, A379623, A379624, A379627. %K A379628 nonn,more %O A379628 1,4 %A A379628 _Omar E. Pol_, Jan 07 2025 %E A379628 a(7)-a(16) from _Pontus von Brömssen_, Jan 11 2025 %E A379628 a(17)-a(18) from _John Mason_, Feb 16 2025