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A354308
Number of free polyjogs with n cells.
0
1, 1, 4, 17, 88, 503, 3071, 19372, 124575, 813020, 5361539, 35662727, 238864272, 1609398564
OFFSET
1,3
COMMENTS
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.
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).
EXAMPLE
a(3) = 4, because there are four ways to adjoin three unit squares by half-edges:
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
Sequence in context: A114190 A135168 A364212 * A357617 A350474 A058279
KEYWORD
nonn,hard,more
AUTHOR
Aaron N. Siegel, May 23 2022
STATUS
approved