A395405 - OEIS

A395405

a(n) is the maximum size of a set family F on {1, 2, ..., n} such that for any pair of not necessarily distinct sets S, T in F, there exists s in S and t in T such that |s - t| = 1.

%I #8 May 08 2026 01:26:19

%S 0,1,3,8,18,41,87,184

%N a(n) is the maximum size of a set family F on {1, 2, ..., n} such that for any pair of not necessarily distinct sets S, T in F, there exists s in S and t in T such that |s - t| = 1.

%C Construct a graph G with subsets of {1, 2, ..., n} as vertices. Vertices S and T (not necessarily distinct) are connected iff there exists s in S and t in T such that |s - t| = 1. a(n) is the size of the maximum clique in G.

%H Yifan Xie, <a href="/A395405/a395405.py.txt">Python program</a>

%e For n = 3, the set family {{1, 2}, {2, 3}, {1, 2, 3}} is the largest because all other subsets are isolated vertices in G.

%o (Python) # See links.

%Y Cf. A394221.

%K nonn,more

%O 1,3

%A _Yifan Xie_, Apr 21 2026