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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.

%I A157608 #16 Aug 31 2024 15:14:36
%S A157608 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 A157608 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 A157608 153,320,323,87,2,0,0,1,3,11,44,177,514,896,723,142,2,0,0
%N A157608 Array read by antidiagonals, giving number of fixed hexagonal polyominoes of height up to n/2 and with hexagonal cell count k.
%H A157608 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 A157608 Moa Apagodu, <a href="https://web.archive.org/web/20160910051723/https://www.people.vcu.edu/~mapagodu/programs.html">Maple programs</a>.
%F A157608 T(n, k) = A001207(k) for n >= 2*k. - _Andrey Zabolotskiy_, Aug 31 2024
%e A157608 The array begins:
%e A157608 ================================================
%e A157608 n=1 | 0 | 0 |  0 |  0 |   0 |   0 |   0 |    0 |
%e A157608 n=2 | 1 | 0 |  0 |  0 |   0 |   0 |   0 |    0 |
%e A157608 n=3 | 1 | 2 |  2 |  2 |   2 |   2 |   2 |    2 |
%e A157608 n=4 | 1 | 3 |  6 | 11 |  19 |  32 |  53 |   87 |
%e A157608 n=5 | 1 | 3 | 10 | 25 |  61 | 142 | 323 |  723 |
%e A157608 n=6 | 1 | 3 | 11 | 37 | 111 | 320 | 896 | 2461 |
%e A157608 ================================================
%p A157608 T(4, 4) = 11:
%p A157608      _   _   _   _     _               _      _       _
%p A157608    _/ \_/ \ / \_/ \_  / \_   _   _   _/ \   _/ \_   _/ \_
%p A157608   / \_/ \_/ \_/ \_/ \ \_/ \_/ \ / \_/ \_/ _/ \_/ \ / \_/ \_
%p A157608   \_/ \_/     \_/ \_/   \_/ \_/ \_/ \_/  / \_/ \_/ \_/ \_/ \
%p A157608                           \_/     \_/    \_/             \_/
%p A157608      _     _   _    _   _      _    _
%p A157608    _/ \_  / \_/ \  / \_/ \   _/ \  / \_
%p A157608   / \_/ \ \_/ \_/  \_/ \_/ _/ \_/  \_/ \_
%p A157608   \_/ \_/   \_/ \  / \_/  / \_/ \  / \_/ \
%p A157608     \_/       \_/  \_/    \_/ \_/  \_/ \_/
%Y A157608 Cf. A001170, A001207, A059716, A068091, A308359.
%K A157608 nonn,tabl
%O A157608 1,8
%A A157608 _Jonathan Vos Post_, Mar 02 2009
%E A157608 Definition not clear to me! "Height" refers to the lattice or to the polyominoes? - _N. J. A. Sloane_, Mar 14 2009
%E A157608 Name clarified and more terms added by _Andrey Zabolotskiy_, Aug 24 2024