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 A354308 #8 May 24 2022 02:18:45 %S A354308 1,1,4,17,88,503,3071,19372,124575,813020,5361539,35662727,238864272, %T A354308 1609398564 %N A354308 Number of free polyjogs with n cells. %C A354308 A polyjog is a polyform composed of n connected unit squares adjoined along half-edges: every pair of adjacent cells shares an edge of length exactly 1/2. The polyjogs of order n form a subset of polyominoes of order 4n. %C A354308 Figures that differ by a rotation or reflection are considered equivalent. %C A354308 It is not hard to prove that every polyjog can be tiled by unit squares in exactly one way. Therefore, equivalences involving internal rearrangement of unit squares are not relevant (unlike related sequences; cf. A216583). %H A354308 George Sicherman, <a href="http://www.recmath.org/PolyCur/polyjogs/">Catalogue of Polyjogs</a> %e A354308 a(3) = 4, because there are four ways to adjoin three unit squares by half-edges: %e A354308 aa cc cc aa aa %e A354308 aabbcc aa cc aabb aa %e A354308 bb aabb bbcc bb %e A354308 bb cc bbcc %e A354308 cc %e A354308 (In these figures, the three unit squares are depicted by 2 X 2 arrangements of letters a, b, and c.) %Y A354308 Cf. A000105, A216583. %K A354308 nonn,hard,more %O A354308 1,3 %A A354308 _Aaron N. Siegel_, May 23 2022