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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 (list; graph; refs; listen; history; text; internal format)
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).
LINKS
George Sicherman, Catalogue of Polyjogs
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

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Last modified April 15 13:47 EDT 2024. Contains 371689 sequences. (Running on oeis4.)