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 A379629 #27 Feb 21 2025 11:45:16 %S A379629 1,2,5,15,41,139,474,1773,6686,26043,101814,402297,1593124,6332329, %T A379629 25200575,100462874,400908688,1601541747 %N A379629 Sum of the lengths of the free polyominoes with n cells. %C A379629 The length here is the longer of the two dimensions. %H A379629 <a href="/index/Pol#polyominoes">Index entries for sequences related to polyominoes</a>. %e A379629 For n = 4 the free polyominoes with four cells are also called free tetrominoes. %e A379629 The five free tetrominoes are as shown below: %e A379629 _ %e A379629 _ _ _ |_| %e A379629 _ _ |_| |_|_ |_|_ |_| %e A379629 |_|_| |_|_ |_|_| |_|_| |_| %e A379629 |_|_| |_|_| |_| |_| |_| %e A379629 . %e A379629 There are no free tetrominoes of length 1, there is only one free tetromino of length 2, there are three free tetrominoes of length 3 and there is only one free tetromino of length 4, hence the sum of the lengths is 0 + 2 + 3 + 3 + 3 + 4 = 15, so a(4) = 15. %Y A379629 Row sums of A379638. %Y A379629 Cf. A000105, A379624, A379625, A379626, A379627. %K A379629 nonn,more %O A379629 1,2 %A A379629 _Omar E. Pol_, Jan 16 2025 %E A379629 a(13)-a(16) from _Pontus von Brömssen_, Jan 17 2025 %E A379629 a(17)-a(18) (based on A379624 b-file) from _Pontus von Brömssen_, Feb 21 2025