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A304195
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Number of fully-leafed free tree-like polyominoes of size n.
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2
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1, 1, 2, 1, 1, 2, 12, 3, 1, 6, 74, 11, 2, 21, 408, 40, 4, 76, 2053, 148, 11, 279
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listen;
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OFFSET
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1,3
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COMMENTS
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A free tree-like polyomino of size n is a connected set of n cells in the square lattice, up to translation, rotation and reflection, whose dual graph has no cycles. It is called fully-leafed when it has the maximal number of leaves over all the same sized free tree-like polyominoes.
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LINKS
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Alexandre Blondin Massé, Julien de Carufel, Alain Goupil, and Maxime Samson. Fully-leafed tree-like polyominoes and polycubes. In Combinatorial algorithms, volume 10765 of Lecture Notes of Computer Science, 28th International workshop, IWOCA 2017, Newcastle, NSW, Australia, Springer, 2018.
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EXAMPLE
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a(5) = 1:
. #
. ###
. #
a(6) = 2:
. # . #
. #### . ####
. # . #
a(7) = 12:
. # # . # # . # # . # . # . #
. ### . #### . ##### . ##### . ##### . #####
. # # . # . . # . # . #
.
. # # . # # . # . # . # . #
. #### . #### . # . ## . ## . #####
. # . # . #### . ### . ### . #
. . . # . # . # .
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CROSSREFS
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Cf. A131482 (free tree-like polyominoes), A304197, A304199 (fully-leafed free tree-like polycubes in 3 and 4 dimensions resp.).
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KEYWORD
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nonn,more
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AUTHOR
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STATUS
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approved
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