A068091 Number of board-pair-pile hexagonal polyominoes with n cells.
1, 3, 11, 44, 186, 814, 3648, 16611, 76437, 354112, 1647344, 7682237, 35873310, 167625690, 783470179, 3662035980, 17115684065, 79986841677, 373759118882, 1746296080947
Offset: 1
Examples
This sequence first diverges from A059716 at n = 4. a(4) is 2 greater than A059716(4) because a(4) counts the following 2 fixed polyhexes of 4 cells that contain a column with two contiguous blocks of cells:
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This sequence first diverges from A001207 at n = 7. a(7) is 4 less than A001207(7) because a(7) does not count the following 4 fixed polyhexes of 7 cells that contain a column with more than two contiguous blocks of cells:
_ _ _ _
_/ \ / \_ _/ \ / \_
/ \_/ \_/ \ / \_/ \_/ \
\_/ \_/ \_/ \_/
/ \_ _/ \ / \_ _/ \
\_/ \ / \_/ \_/ \_ _/ \_/
/ \_/ \_/ \ \_/ \ / \_/
\_/ \_/ \_/ \_/
/ \_ _/ \ _/ \ / \_
\_/ \ / \_/ / \_/ \_/ \
\_/ \_/ \_/ \_/
Links
- Moa Apagodu (formerly Mohamud Mohammed) and Stirling Chow, Counting hexagonal lattice animals confined to a strip, arXiv:math/0202295v5 [math.CO], 2009. See Section 7.
- Moa Apagodu, Counting Hexagonal Lattice Animals Using Umbral-Transfer-Matrix Method [dead link]
- Moa Apagodu, Maple programs.
Programs
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Maple
The sequence is generated by a Maple program that accompanies the paper "Counting Hexagonal Lattice Animals using Umbral-Transfer-Matrix Method (UTMM)"