OFFSET
0,8
COMMENTS
The superset/subset relation on P([n]) is defined as: for all A,B in P([n]), A ~ B iff A is a subset of B or B is a subset of A.
LINKS
P. Flajolet and R. Sedgewick, Analytic Combinatorics, 2009; see page 339.
EXAMPLE
1, 1, 1, 1, 1, 1, 1, 1, 1,...
0, 1, 2, 4, 8, 16, 32, 64, 128,...
0, 1, 4, 14, 50, 178, 634, 2258, 8042,...
0, 1, 8, 46, 278, 1666, 9998, 59986, 359918,...
0, 1, 16, 146, 1454, 14230, 139750, 1371494, 13461638,...
MATHEMATICA
(* gives first 7 rows and 11 columns in about 3 minutes *)
Table[a = Subsets[Range[n]]; f[list_] := Map[Apply[SubsetQ, #] &, list];
G = Map[f, Table[Table[{a[[i]], a[[j]]}, {i, 1, 2^n}], {j, 1, 2^n}]] //
Boole; H = (G - IdentityMatrix[2^n]) + Transpose[(G - IdentityMatrix[2^n]) + IdentityMatrix[2^n]]; b = Inverse[IdentityMatrix[2^n] - z H] // Simplify; MatrixForm[b]; nn = 10; CoefficientList[Series[b[[1, 2^n]], {z, 0, nn}], z], {n, 0, 6}] // Grid
CROSSREFS
KEYWORD
nonn,tabl
AUTHOR
Geoffrey Critzer, Jul 31 2020
STATUS
approved