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A157608
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Array read by antidiagonals, giving number of hexagonal polyominoes embedded in the square lattice of height n and their series expansion by hexagonal cell count.
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0
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0, 1, 0, 1, 0, 0, 1, 2, 0, 0, 1, 3, 2, 0, 0, 1, 3, 6, 2, 0, 0, 1, 3, 10, 11, 2, 0, 0
(list;
table;
graph;
refs;
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history;
text;
internal format)
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OFFSET
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1,8
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COMMENTS
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Adapted from M. Mohammed, p.10, Table 1: Generating functions for hexanimals polyominoes embedded in the square lattice of height n and their series expansion by hexagonal cell count. Page 13 gives an unknown sequence 1, 3, 11, 44, 186, 814, 3648, 16611, 76437, 354112, 1647344, 7682237 that enumerates 2-board hexanimals with a given hexagonal cell count, the analog of sequence A001170 for board-pair-pile polyominoes.
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LINKS
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EXAMPLE
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The array begins:
=========================================
n=1.|.0.|.0.|..0.|..0.|...0.|...0.|...0.|.0.|.0.|
n=2.|.1.|.0.|..0.|..0.|...0.|...0.|...0.|.0.|.0.|
n=3.|.1.|.2.|..2.|..2.|...2.|...2.|...2.|.2.|.2.|
n=4.|.1.|.3.|..6.|.11.|..19.|..32.|..53.|.87.|
n=5.|.1.|.3.|.10.|.25.|..61.|.142.|.323.|.723.|
n=6.|.1.|.3.|.11.|.37.|.111.|.320.|.896.|
=========================================
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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Definition not clear to me! "Height" refers to the lattice or to the polyominoes? - N. J. A. Sloane, Mar 14 2009
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STATUS
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approved
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