A381294 Smallest number k such that there are n sets A_1,...,A_n with each A_i being a subset of {1,...,k} and the intersection of A_i and A_j has size |i-j| for all 1 <= i < j <= n.

0, 0, 1, 2, 5, 9, 16, 24, 36, 50, 70, 91, 120, 150, 189, 231, 280, 336, 398, 468, 547, 630, 728

Offset

0,4

Comments

k is in Omega(n^3/2) and O(n^3).

Links

Table of n, a(n) for n=0..22.

Jonas Seiler, Optimal solution sets A_1,..,A_n for each n=0..22

Jonas Seiler, Julia Code for calculating the sequence

Jonas Seiler, Summary of results including upper and lower bounds

Example

For n = 4, k = 5 is optimal with the following solution:
  A_1 = {1,2,3,4},
  A_2 = {1,5},
  A_3 = {1,2},
  A_4 = {1,3,4,5}.

Crossrefs

Sequence in context: A345140 A072829 A169740 * A360419 A282044 A138226

Adjacent sequences: A381291 A381292 A381293 * A381295 A381296 A381297

Keyword

nonn,more

Author

Jonas Seiler, Feb 19 2025

Status

approved