cp's OEIS Frontend

A068091 Number of board-pair-pile hexagonal polyominoes with n cells.

%I A068091 #9 Aug 31 2024 15:12:40
%S A068091 1,3,11,44,186,814,3648,16611,76437,354112,1647344,7682237,35873310,
%T A068091 167625690,783470179,3662035980,17115684065,79986841677,373759118882,
%U A068091 1746296080947
%N A068091 Number of board-pair-pile hexagonal polyominoes with n cells.
%H A068091 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 Section 7.
%H A068091 Moa Apagodu, <a href="http://www.math.rutgers.edu/umbralm1.html">Counting Hexagonal Lattice Animals Using Umbral-Transfer-Matrix Method</a> [dead link]
%H A068091 Moa Apagodu, <a href="https://web.archive.org/web/20160910051723/https://www.people.vcu.edu/~mapagodu/programs.html">Maple programs</a>.
%e A068091 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:
%e A068091      _    _
%e A068091    _/ \  / \_
%e A068091   / \_/  \_/ \
%e A068091   \_/      \_/
%e A068091   / \_    _/ \
%e A068091   \_/ \  / \_/
%e A068091     \_/  \_/
%e A068091 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:
%e A068091      _    _        _        _
%e A068091    _/ \  / \_    _/ \      / \_
%e A068091   / \_/  \_/ \  / \_/      \_/ \
%e A068091   \_/      \_/  \_/          \_/
%e A068091   / \_    _/ \  / \_        _/ \
%e A068091   \_/ \  / \_/  \_/ \_    _/ \_/
%e A068091   / \_/  \_/ \    \_/ \  / \_/
%e A068091   \_/      \_/      \_/  \_/
%e A068091   / \_    _/ \     _/ \  / \_
%e A068091   \_/ \  / \_/    / \_/  \_/ \
%e A068091     \_/  \_/      \_/      \_/
%p A068091 The sequence is generated by a Maple program that accompanies the paper "Counting Hexagonal Lattice Animals using Umbral-Transfer-Matrix Method (UTMM)"
%Y A068091 Cf. A001170, A001207, A059716, A157608.
%K A068091 hard,more,nonn
%O A068091 1,2
%A A068091 _Moa Apagodu_, Mar 22 2002 and Oct 31 2002