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

1,2

Links

Table of n, a(n) for n=1..20.

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.

Example

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:
     _    _
   _/ \  / \_
  / \_/  \_/ \
  \_/      \_/
  / \_    _/ \
  \_/ \  / \_/
    \_/  \_/
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:
     _    _        _        _
   _/ \  / \_    _/ \      / \_
  / \_/  \_/ \  / \_/      \_/ \
  \_/      \_/  \_/          \_/
  / \_    _/ \  / \_        _/ \
  \_/ \  / \_/  \_/ \_    _/ \_/
  / \_/  \_/ \    \_/ \  / \_/
  \_/      \_/      \_/  \_/
  / \_    _/ \     _/ \  / \_
  \_/ \  / \_/    / \_/  \_/ \
    \_/  \_/      \_/      \_/

Maple

The sequence is generated by a Maple program that accompanies the paper "Counting Hexagonal Lattice Animals using Umbral-Transfer-Matrix Method (UTMM)"

Crossrefs

Cf. A001170, A001207, A059716, A157608.

Sequence in context: A167012 A167013 A121220 * A001207 A319156 A026887

Adjacent sequences: A068088 A068089 A068090 * A068092 A068093 A068094

Keyword

hard,more,nonn

Author

Moa Apagodu, Mar 22 2002 and Oct 31 2002

Status

approved