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 A379627 #39 Feb 16 2025 17:19:31 %S A379627 1,2,7,26,95,353,1387,5699,23592,99020,415796,1748722,7336978, %T A379627 30741661,128510698,536268877,2233642396,9288889882 %N A379627 Total area of the bounding boxes of the free polyominoes with n cells. %C A379627 a(n) is also the total sum of all products of length and width of the free polyominoes with n cells. %H A379627 <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>. %F A379627 a(n) = A057766(n) + A379628(n). %e A379627 Illustration for n = 4: %e A379627 The free polyominoes with four cells are also called free tetrominoes. %e A379627 The five free tetrominoes are as shown below: %e A379627 _ %e A379627 |_| _ _ _ %e A379627 |_| |_| |_|_ |_|_ _ _ %e A379627 |_| |_|_ |_|_| |_|_| |_|_| %e A379627 |_| |_|_| |_| |_| |_|_| %e A379627 . %e A379627 The bounding boxes are respectively as shown below: %e A379627 _ %e A379627 | | _ _ _ _ _ _ %e A379627 | | | | | | | | _ _ %e A379627 | | | | | | | | | | %e A379627 |_| |_ _| |_ _| |_ _| |_ _| %e A379627 . %e A379627 4 X 1 3 X 2 3 X 2 3 X 2 2 X 2 %e A379627 . %e A379627 The total area of the bounding boxes is 4 + 6 + 6 + 6 + 4 = 26, so a(4) = 26. %e A379627 . %Y A379627 Cf. A000105, A057766, A379623, A379624, A379628. %K A379627 nonn,more %O A379627 1,2 %A A379627 _Omar E. Pol_, Jan 07 2025 %E A379627 a(7)-a(16) from _Pontus von Brömssen_, Jan 11 2025 %E A379627 a(17)-a(18) from _John Mason_, Feb 16 2025