A376828 a(n) = smallest integer k >= 0 such that there exist n disjoint partitions of k that yield the same multinomial coefficient.

0, 7, 31, 50

Offset: 1

Author

Pontus von Brömssen, Oct 05 2024

Keywords

• nonn
• hard
• more

Comments

a(5) > 153 if it exists. - Max Alekseyev, May 18 2025

Examples

			a(2) = 7 is the smallest k such that A376821(k) > 0.
    |       | n partitions of a(n) with a common multinomial coefficient
  n |  a(n) |  but no part appearing in more than one of the partitions
  --+-------+-----------------------------------------------------------
  1 |    0  | ()
  2 |    7  | (1,1,1,4), (2,2,3)
  3 |   31  | (1,1,4,4,4,7,10), (2,2,2,2,5,9,9), (3,3,3,6,8,8)
  4 |   50  | (1,1,1,9,12,26), (2,2,8,11,27), (3,3,3,16,25), (5,6,15,24)
		

Crossrefs

Cf. A376661, A376673, A376821, A376866.

Extensions

Name edited by Max Alekseyev, May 18 2025