A157608 Array read by antidiagonals, giving number of fixed hexagonal polyominoes of height up to n/2 and with hexagonal cell count k.

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

Author

Jonathan Vos Post, Mar 02 2009

Keywords

• nonn
• tabl

Examples

			The array begins:
================================================
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 |
================================================
		

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.

Crossrefs

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

Programs

Maple

T(4, 4) = 11:
                                               
   / \/ \ / \/ \  / \         / \   / \   / \
  / \/ \/ \/ \/ \ \/ \/ \ / \/ \/ / \/ \ / \/ \
  \/ \/     \/ \/   \/ \/ \/ \/  / \/ \/ \/ \/ \
                          \/     \/    \/             \/
                              _
   / \  / \/ \  / \/ \   / \  / \
  / \/ \ \/ \/  \/ \/ / \/  \/ \_
  \/ \/   \/ \  / \/  / \/ \  / \/ \
    \/       \/  \/    \/ \/  \/ \_/

Formula

T(n, k) = A001207(k) for n >= 2*k. - Andrey Zabolotskiy, Aug 31 2024

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