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.

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

Offset

1,3

Comments

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.

Links

Table of n, a(n) for n=1..8.

Yifan Xie, Python program

Example

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.

Prog

(Python) # See links.

Crossrefs

Cf. A394221.

Sequence in context: A117080 A240135 A066425 * A026679 A371682 A191524

Adjacent sequences: A395402 A395403 A395404 * A395406 A395407 A395408

Keyword

nonn,more

Author

Yifan Xie, Apr 21 2026

Status

approved