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A056841
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Number of diagonal polyominoes with n cells.
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6
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1, 1, 2, 5, 15, 54, 212, 908, 4011, 18260, 84320, 394462, 1860872, 8843896, 42275308, 203113670, 980101070, 4747504560, 23074132601
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OFFSET
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1,3
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COMMENTS
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Apparently the cells are circular blobs which must be connected diagonally and the polyominoes can be rotated by 90 degrees and turned over.
Also the number of essentially different (i.e., not related by reflections, translations or rotations) diagrams consisting of n nodes in Z^2 and n-1 horizontal or vertical edges of length 1 between pairs of nodes such that the resulting graph is connected (hence a tree). - Paul Boddington, Jul 27 2004
They are thus equivalent to a subset of the polyedges, counted by A019988, i.e., those that are treelike. - John Mason, Aug 20 2021
The number of treelike polyedges with n edges is a(n+1). - John Mason, Feb 12 2023
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LINKS
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FORMULA
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EXAMPLE
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The diagonal polyominoes with 1, 2, 3 and 4 cells are
O O O O O
\ \ \ /
O O O
\
O
O O O O O O
\ \ \ / \ / /
O O O O O O O
\ / \ \ / /
O O O O O
\ \
O O
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CROSSREFS
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KEYWORD
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nonn,nice,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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