cp's OEIS Frontend

A270952 T(n, k) is the number of k-element connected subposets of the n-th Boolean lattice, 0 <= k <= 2^n.

%I A270952 #18 Feb 16 2025 08:33:32
%S A270952 1,1,1,2,1,1,4,5,4,1,1,8,19,42,61,56,28,8,1,1,16,65,304,1129,3200,
%T A270952 6775,10680,12600,11386,8002,4368,1820,560,120,16,1,1,32,211,1890,
%U A270952 14935,97470
%N A270952 T(n, k) is the number of k-element connected subposets of the n-th Boolean lattice, 0 <= k <= 2^n.
%C A270952 The n-th Boolean lattice is the set of all subsets of {1,2,...,n}, partially ordered by inclusion.
%H A270952 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/BooleanAlgebra.html">Boolean Algebra</a>.
%e A270952 The triangle begins:
%e A270952 n\k 0  1   2    3     4     5    6     7     8     9   10   11   12  13  14
%e A270952 0   1  1
%e A270952 1   1  2   1
%e A270952 2   1  4   5    4     1
%e A270952 3   1  8  19   42    61    56   28     8     1
%e A270952 4   1 16  65  304  1129  3200 6775 10680 12600 11386 8002 4368 1820 560 120
%e A270952 5   1 32 211 1890 14935 97470  ...
%e A270952 For T(2, 2) = 5: [{},{1}], [{},{2}], [{},{1,2}], [{1},{1,2}], [{2},{1,2}].
%o A270952 (Sage)
%o A270952 def ConnectedSubs(n): # Returns row n of T(n, k).
%o A270952     Bn = posets.BooleanLattice(n)
%o A270952     counts = [0]*(2^n+1)
%o A270952     for X in Subsets(range(2^n)):
%o A270952         if Bn.subposet(X).is_connected():
%o A270952             counts[len(X)] += 1
%o A270952     return counts
%Y A270952 Columns: A000012 (k = 0, 2^n), A000079 (k = 1, 2^n - 1), A001047 (k = 3).
%K A270952 nonn,more,tabf
%O A270952 0,4
%A A270952 _Danny Rorabaugh_, Mar 26 2016