A221494 Table T(n,k) = number of skeleta of (3+1)-free posets with n clone sets and k tangles

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

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: A077021 A344437 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