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

1,8

Links

Table of n, a(n) for n=1..78.

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:
================================================
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 |
================================================

Maple

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

Crossrefs

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

Sequence in context: A175045 A292377 A216238 * A220062 A216054 A217257

Adjacent sequences: A157605 A157606 A157607 * A157609 A157610 A157611

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