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A274109
Triangle read by rows: T(n,k) = number of partitions of n into exactly k parts with exactly two different sizes, the sizes being relatively prime (n >= 3, 2 <= k <= n-1).
2
1, 1, 1, 2, 2, 1, 1, 1, 2, 1, 3, 3, 2, 2, 1, 2, 2, 2, 2, 2, 1, 3, 3, 2, 3, 2, 2, 1, 2, 2, 4, 1, 3, 2, 2, 1, 5, 5, 3, 4, 2, 3, 2, 2, 1, 2, 2, 2, 2, 3, 2, 3, 2, 2, 1, 6, 6, 4, 5, 2, 4, 2, 3, 2, 2, 1, 3, 3, 5, 3, 4, 1, 4, 2, 3, 2, 2, 1, 4, 4, 3, 3, 4, 4, 2, 4, 2, 3, 2, 2, 1, 4, 4, 5, 3, 4, 3, 3, 2, 4, 2, 3, 2, 2, 1, 8, 8, 5, 7, 3, 5, 3, 4, 2, 4, 2, 3, 2, 2, 1, 3, 3, 5, 2, 5, 2, 4, 2, 4, 2, 4, 2, 3, 2, 2, 1, 9, 9, 6, 7, 3, 7, 3, 4, 3, 4, 2, 4, 2, 3, 2, 2, 1
OFFSET
3,4
LINKS
N. Benyahia Tani, S. Bouroubi, and O. Kihel, An effective approach for integer partitions using exactly two distinct sizes of parts, Bulletin du Laboratoire 03 (2015), 18-27.
N. Benyahia Tani, S. Bouroubi, and O. Kihel, An effective approach for integer partitions using exactly two distinct sizes of parts, Elemente der Mathematik 72(2) (2017), 66-74.
EXAMPLE
Triangle T(n,k) (with columns n >= 3 and k >= 2) begins as follows:
1;
1, 1;
2, 2, 1;
1, 1, 2, 1;
3, 3, 2, 2, 1;
2, 2, 2, 2, 2, 1;
3, 3, 2, 3, 2, 2, 1;
2, 2, 4, 1, 3, 2, 2, 1;
5, 5, 3, 4, 2, 3, 2, 2, 1;
2, 2, 2, 2, 3, 2, 3, 2, 2, 1;
6, 6, 4, 5, 2, 4, 2, 3, 2, 2, 1;
3, 3, 5, 3, 4, 1, 4, 2, 3, 2, 2, 1;
4, 4, 3, 3, 4, 4, 2, 4, 2, 3, 2, 2, 1;
...
CROSSREFS
Row sums give A274108.
Sequence in context: A064892 A236344 A333124 * A083019 A137865 A052494
KEYWORD
nonn,tabl
AUTHOR
N. J. A. Sloane, Jun 17 2016
STATUS
approved