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A221494 Table T(n,k) = number of skeleta of (3+1)-free posets with n clone sets and k tangles 2
1, 1, 1, 3, 5, 1, 12, 28, 16, 2, 55, 165, 152, 47, 4, 273, 1001, 1265, 658, 136, 9, 1428, 6188, 9919, 7315, 2547, 392, 21, 7752, 38760, 75208, 71981, 35975, 9252, 1130, 51, 43263, 245157, 558144, 657356, 431599, 159701, 32286, 3262, 127, 246675, 1562275 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..46.

M. Guay-Paquet, A. H. Morales, E. Rowland, Structure and enumeration of (3+1)-free posets (extended abstract), arXiv:1212.5356 [math.CO], 2012.

FORMULA

G.f.: S(x, y) is the unique power series solution of the equation S(x, y) = 1 + S(x, y)^2 * x / (1 + x) + S(x, y)^3 * y.

EXAMPLE

There are 28 skeleta of (3+1)-free posets with 1 clone set and 2 tangles.

Table begins

1   1    3     12      55      273 ...

1   5   28    165    1001     6188 ...

1  16  152   1265    9919    75208 ...

2  47  658   7315   71981   657356 ...

4 136 2547  35975  431599  4660516 ...

9 392 9252 159701 2277821 28589750 ...

......................................

CROSSREFS

Cf. A079145, A079146, A221492, A221493

Sequence in context: A138259 A077021 A143250 * A174883 A084833 A204020

Adjacent sequences:  A221491 A221492 A221493 * A221495 A221496 A221497

KEYWORD

nonn,easy,tabl

AUTHOR

Mathieu Guay-Paquet, Jan 18 2013

STATUS

approved

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Last modified May 26 00:32 EDT 2020. Contains 334613 sequences. (Running on oeis4.)