A376821 Number of irreducible pairs of partitions of n.

0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 1, 0, 0, 3, 3, 6, 7, 8, 4, 6, 7, 12, 17, 23, 23, 31, 38, 36, 70, 71, 101, 127, 118, 145, 191, 209, 261, 309, 396, 462, 512, 652, 769, 878, 1097, 1320, 1563, 1827, 2098, 2533, 2932, 3475, 4185, 4756, 5726, 6614, 7686, 9189, 10825

Offset: 0

Author

Pontus von Brömssen, Oct 05 2024

Keywords

• nonn

Comments

A pair of partitions of n is irreducible if the two partitions yield the same multinomial coefficient but have no parts in common. The partitions in the pair are required to be distinct, otherwise a(0) would be 1.

Examples

			   n | irreducible pairs of partitions of n
  ---+-------------------------------------
   7 | (1,1,1,4), (2,2,3)
   8 | (1,1,6), (3,5)
  10 | (1,4,5), (2,2,6)
  13 | (1,1,1,10), (6,7)
     | (1,1,3,8), (2,4,7)
     | (1,1,1,1,1,8), (2,2,2,7)
  14 | (1,2,2,9), (3,3,8)
     | (1,1,1,2,9), (3,4,7)
     | (1,1,1,1,1,1,4,4), (2,2,2,2,3,3)
		

Links

• George E. Andrews, Arnold Knopfmacher, and Burkhard Zimmermann, On the number of distinct multinomial coefficients, Journal of Number Theory 118 (2006), 15-30; arXiv preprint, arXiv:math/0509470 [math.CO], 2005. (See Section 7.)

Crossrefs

Cf. A070289, A260669, A325306, A376661.