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A365654
Number of free n-polyominoids, allowing right-angled connections only ("hard" polyominoids).
6
1, 1, 5, 16, 90, 537, 3826, 28655
OFFSET
1,3
COMMENTS
Two squares are allowed to meet in a straight 180-degree connection, but the structure must be connected through right-angled ("hard") connections only. This seems to be in agreement with the definition of "hard" polyominoids in the Mireles Jasso link (the number of fixed hard hexominoids given by the "sample report" linked from that web-page agrees with A365655(6) = 22417), but differs from the definition in the Wikipedia article. The smallest example of a polyominoid that is included here but is not hard according to Wikipedia consists of two squares between (0,0,1) and (2,1,1), two between (0,0,1) and (2,0,2), and one between (1,0,0) and (1,1,1) (a "one-legged sofa", see illustration in the Mireles Jasso link). This explains why a(5) = 90, while the number of hard pentominoids is 89 according to the Wikipedia article.
Equivalently, number of n-polysticks in 3 dimensions, connected through right-angled connections.
CROSSREFS
13th and 17th row of A366766.
Cf. A075679 (polyominoids), A365559 (polysticks in 3 dimensions), A365655 (fixed).
Sequence in context: A286077 A286072 A002830 * A370096 A196015 A332625
KEYWORD
nonn,hard,more
AUTHOR
STATUS
approved