cp's OEIS Frontend

A374819 Triangle read by rows: T(n,k) is the number of functions on the Boolean lattice B_n satisfying f({}) =0, f([n])=k, and the Boolean growth rule: f(J union {i})-f(J) in {0,1} for all subsets J of [n]={1, ..., n} and all i in [n]\J, 0 <= k <= n.

%I A374819 #16 Dec 12 2024 15:30:49
%S A374819 1,1,1,1,4,1,1,18,18,1,1,166,656,166,1,1,7579,189967,189967,7579,1,1,
%T A374819 7828352
%N A374819 Triangle read by rows: T(n,k) is the number of functions on the Boolean lattice B_n satisfying f({}) =0, f([n])=k, and the Boolean growth rule: f(J union {i})-f(J) in {0,1}  for all subsets J of [n]={1, ..., n} and all i in [n]\J, 0 <= k <= n.
%C A374819 For k=1, these numbers are the Dedekind numbers A007153 counting the number of monotone Boolean functions or equivalently antichains of subsets of an n-set containing at least one nonempty set.
%H A374819 Sara Billey and Matjaž Konvalinka, <a href="https://arxiv.org/abs/2412.03236">Generalized rank functions and quilts of alternating sign matrices</a>, arXiv:2412.03236 [math.CO], 2024. See p. 32.
%e A374819 Triangle begins:
%e A374819   1;
%e A374819   1,    1;
%e A374819   1,    4,      1;
%e A374819   1,   18,     18,      1;
%e A374819   1,  166,    656,    166,    1;
%e A374819   1, 7579, 189967, 189967, 7579, 1;
%e A374819   ...
%Y A374819 Cf. A000372, A007153, A374820, A374821, A374822, A297622, A374824.
%K A374819 nonn,tabl,more
%O A374819 0,5
%A A374819 _Sara Billey_ and _Matjaz Konvalinka_, Jul 25 2024