A394221 a(n) is the maximum size of a set family F on {1, 2, ..., n} such that for any pair of distinct sets S, T in F, there exists s in S and t in T such that |s - t| = 1.

1, 3, 5, 11, 22, 46, 94, 193

Offset

1,2

Comments

Construct a graph G with subsets of {1, 2, ..., n} as vertices. Distinct vertices S and T 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 {{2}, {1,2}, {2,3}, {1,3}, {1,2,3}} satisfies the conditions. On the other hand, at most one of the sets {1}, {3} and {1,3} can belong to the family, and the empty set cannot appear, so the size is at most 5. Hence a(3) = 5.

Prog

(Python) # See links.

Crossrefs

Cf. A395405.

Sequence in context: A293338 A168655 A391600 * A005830 A007008 A018110

Adjacent sequences: A394218 A394219 A394220 * A394222 A394223 A394224

Keyword

nonn,more

Author

Yifan Xie, Apr 10 2026

Status

approved