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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
OFFSET
0,4
LINKS
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
KEYWORD
nonn,easy,tabl
AUTHOR
Mathieu Guay-Paquet, Jan 18 2013
STATUS
approved