%I #8 May 24 2022 02:18:45
%S 1,1,4,17,88,503,3071,19372,124575,813020,5361539,35662727,238864272,
%T 1609398564
%N Number of free polyjogs with n cells.
%C A polyjog is a polyform composed of n connected unit squares adjoined along halfedges: 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 Figures that differ by a rotation or reflection are considered equivalent.
%C 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 George Sicherman, <a href="http://www.recmath.org/PolyCur/polyjogs/">Catalogue of Polyjogs</a>
%e a(3) = 4, because there are four ways to adjoin three unit squares by halfedges:
%e aa cc cc aa aa
%e aabbcc aa cc aabb aa
%e bb aabb bbcc bb
%e bb cc bbcc
%e cc
%e (In these figures, the three unit squares are depicted by 2 X 2 arrangements of letters a, b, and c.)
%Y Cf. A000105, A216583.
%K nonn,hard,more
%O 1,3
%A _Aaron N. Siegel_, May 23 2022
