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A376821
Number of irreducible pairs of partitions of n.
1
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
0,14
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.
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.)
EXAMPLE
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)
CROSSREFS
KEYWORD
nonn
AUTHOR
STATUS
approved