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A157608
Array read by antidiagonals, giving number of fixed hexagonal polyominoes of height up to n/2 and with hexagonal cell count k.
1
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, 1, 3, 11, 25, 19, 2, 0, 0, 1, 3, 11, 37, 61, 32, 2, 0, 0, 1, 3, 11, 43, 111, 142, 53, 2, 0, 0, 1, 3, 11, 44, 153, 320, 323, 87, 2, 0, 0, 1, 3, 11, 44, 177, 514, 896, 723, 142, 2, 0, 0
OFFSET
1,8
LINKS
Moa Apagodu (formerly Mohamud Mohammed) and Stirling Chow, Counting hexagonal lattice animals confined to a strip, arXiv:math/0202295v5 [math.CO], 2009. See Table 1.
Moa Apagodu, Maple programs.
FORMULA
T(n, k) = A001207(k) for n >= 2*k. - Andrey Zabolotskiy, Aug 31 2024
EXAMPLE
The array begins:
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n=1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
n=2 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |
n=3 | 1 | 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 | 2461 |
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MAPLE
T(4, 4) = 11:
_ _ _ _ _ _ _ _
_/ \_/ \ / \_/ \_ / \_ _ _ _/ \ _/ \_ _/ \_
/ \_/ \_/ \_/ \_/ \ \_/ \_/ \ / \_/ \_/ _/ \_/ \ / \_/ \_
\_/ \_/ \_/ \_/ \_/ \_/ \_/ \_/ / \_/ \_/ \_/ \_/ \
\_/ \_/ \_/ \_/
_ _ _ _ _ _ _
_/ \_ / \_/ \ / \_/ \ _/ \ / \_
/ \_/ \ \_/ \_/ \_/ \_/ _/ \_/ \_/ \_
\_/ \_/ \_/ \ / \_/ / \_/ \ / \_/ \
\_/ \_/ \_/ \_/ \_/ \_/ \_/
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Jonathan Vos Post, Mar 02 2009
EXTENSIONS
Definition not clear to me! "Height" refers to the lattice or to the polyominoes? - N. J. A. Sloane, Mar 14 2009
Name clarified and more terms added by Andrey Zabolotskiy, Aug 24 2024
STATUS
approved