

A354308


Number of free polyjogs with n cells.


0



1, 1, 4, 17, 88, 503, 3071, 19372, 124575, 813020, 5361539, 35662727, 238864272, 1609398564
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OFFSET

1,3


COMMENTS

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.
Figures that differ by a rotation or reflection are considered equivalent.
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).


LINKS



EXAMPLE

a(3) = 4, because there are four ways to adjoin three unit squares by halfedges:
aa cc cc aa aa
aabbcc aa cc aabb aa
bb aabb bbcc bb
bb cc bbcc
cc
(In these figures, the three unit squares are depicted by 2 X 2 arrangements of letters a, b, and c.)


CROSSREFS



KEYWORD

nonn,hard,more


AUTHOR



STATUS

approved



