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Array read by antidiagonals, giving number of fixed hexagonal polyominoes of height up to n/2 and with hexagonal cell count k.
1

%I #16 Aug 31 2024 15:14:36

%S 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,

%T 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,

%U 153,320,323,87,2,0,0,1,3,11,44,177,514,896,723,142,2,0,0

%N Array read by antidiagonals, giving number of fixed hexagonal polyominoes of height up to n/2 and with hexagonal cell count k.

%H Moa Apagodu (formerly Mohamud Mohammed) and Stirling Chow, <a href="https://arxiv.org/abs/math/0202295">Counting hexagonal lattice animals confined to a strip</a>, arXiv:math/0202295v5 [math.CO], 2009. See Table 1.

%H Moa Apagodu, <a href="https://web.archive.org/web/20160910051723/https://www.people.vcu.edu/~mapagodu/programs.html">Maple programs</a>.

%F T(n, k) = A001207(k) for n >= 2*k. - _Andrey Zabolotskiy_, Aug 31 2024

%e The array begins:

%e ================================================

%e n=1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

%e n=2 | 1 | 0 | 0 | 0 | 0 | 0 | 0 | 0 |

%e n=3 | 1 | 2 | 2 | 2 | 2 | 2 | 2 | 2 |

%e n=4 | 1 | 3 | 6 | 11 | 19 | 32 | 53 | 87 |

%e n=5 | 1 | 3 | 10 | 25 | 61 | 142 | 323 | 723 |

%e n=6 | 1 | 3 | 11 | 37 | 111 | 320 | 896 | 2461 |

%e ================================================

%p T(4, 4) = 11:

%p _ _ _ _ _ _ _ _

%p _/ \_/ \ / \_/ \_ / \_ _ _ _/ \ _/ \_ _/ \_

%p / \_/ \_/ \_/ \_/ \ \_/ \_/ \ / \_/ \_/ _/ \_/ \ / \_/ \_

%p \_/ \_/ \_/ \_/ \_/ \_/ \_/ \_/ / \_/ \_/ \_/ \_/ \

%p \_/ \_/ \_/ \_/

%p _ _ _ _ _ _ _

%p _/ \_ / \_/ \ / \_/ \ _/ \ / \_

%p / \_/ \ \_/ \_/ \_/ \_/ _/ \_/ \_/ \_

%p \_/ \_/ \_/ \ / \_/ / \_/ \ / \_/ \

%p \_/ \_/ \_/ \_/ \_/ \_/ \_/

%Y Cf. A001170, A001207, A059716, A068091, A308359.

%K nonn,tabl

%O 1,8

%A _Jonathan Vos Post_, Mar 02 2009

%E Definition not clear to me! "Height" refers to the lattice or to the polyominoes? - _N. J. A. Sloane_, Mar 14 2009

%E Name clarified and more terms added by _Andrey Zabolotskiy_, Aug 24 2024