A221494 Table read by downward diagonals: 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
Examples
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 ... ......................................
Links
- M. Guay-Paquet, A. H. Morales, and 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.