Moa Apagodu - cp's OEIS frontend

User: Moa Apagodu

Moa Apagodu has authored 2 sequences.

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

Moa Apagodu, Mar 22 2002 and Oct 31 2002

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

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.

Cf. A001170, A001207, A059716, A157608.

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

A053617 Number of permutations of length n which avoid the patterns 1234 and 1324.

Original entry on oeis.org

1, 1, 2, 6, 22, 90, 396, 1837, 8864, 44074, 224352, 1163724, 6129840, 32703074, 176351644, 959658200, 5262988330, 29057961666, 161374413196, 900792925199, 5050924332096, 28434661250454, 160644331001476, 910455895039056, 5174722258676440, 29486753617569684

Offset: 0

Moa Apagodu, Mar 20 2000

nonn

These permutations have an "enumeration scheme" of depth 4, see D. Zeilberger's article in the links.
G.f. conjectured to be non-D-finite (see Albert et al. link). - Jay Pantone, Oct 01 2015
a(n) is the number of permutations of length n avoiding the partially ordered pattern (POP) {1>2, 1>3, 2>4, 3>4} of length 4. That is, the number of length n permutations having no subsequences of length 4 in which the first element is the largest and the fourth element is the smallest. - Sergey Kitaev, Dec 10 2020

Andrew Baxter and Jay Pantone, Table of n, a(n) for n = 0..600 (terms n=1..100 from Andrew Baxter)
Michael H. Albert, Cheyne Homberger, Jay Pantone, Nathaniel Shar, Vincent Vatter, Generating Permutations with Restricted Containers, arXiv:1510.00269 [math.CO], 2015.
Alice L. L. Gao, Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, arXiv:1903.08946 [math.CO], 2019.
Alice L. L. Gao, Sergey Kitaev, On partially ordered patterns of length 4 and 5 in permutations, The Electronic Journal of Combinatorics 26(3) (2019), P3.26.
Kremer, Darla and Shiu, Wai Chee, Finite transition matrices for permutations avoiding pairs of length four patterns, Discrete Math. 268 (2003), 171-183. MR1983276 (2004b:05006). See Table 1.
Wikipedia, Permutation classes avoiding two patterns of length 4.
D. Zeilberger, Enumeration schemes and more importantly their automatic generation, Annals of Combinatorics 2 (1998) 185-195. The link is to an overview on Doron Zeilberger's home page; there is a local copy here [Pdf file only, no active links]

Cf. A032351, A053614, A106228, A165542, A165545, A257561, A257562.

More terms from Andrew Baxter, May 20 2011

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User: Moa Apagodu

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

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