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A304869
Triangle read by rows: T(n, k) gives the number of partitions (d1,d2,...,dk) of n such that 0 < d1/1 <= d2/2 <= ... <= dk/k for 1 <= k <= A003056(n).
2
1, 1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 3, 2, 1, 3, 2, 1, 1, 3, 3, 1, 1, 4, 4, 1, 1, 4, 4, 2, 1, 4, 5, 2, 1, 5, 6, 3, 1, 1, 5, 7, 4, 1, 1, 5, 8, 5, 1, 1, 6, 9, 6, 2, 1, 6, 10, 7, 2, 1, 6, 11, 9, 3, 1, 7, 13, 10, 4, 1, 1, 7, 14, 12, 5, 1, 1, 7, 15, 14, 6, 1
OFFSET
1,10
LINKS
EXAMPLE
The partitions (d1,d2) of 9 such that 0 < d1/1 <= d2/2 are (1, 8), (2, 7) and (3, 6). So T(9, 2) = 3.
First few rows are:
1;
1;
1, 1;
1, 1;
1, 1;
1, 2, 1;
1, 2, 1;
1, 2, 1;
1, 3, 2;
1, 3, 2, 1;
1, 3, 3, 1;
1, 4, 4, 1;
1, 4, 4, 2;
1, 4, 5, 2;
1, 5, 6, 3, 1;
CROSSREFS
Row sums give A053282.
Cf. A304871.
Sequence in context: A082647 A367627 A214018 * A161071 A161110 A161045
KEYWORD
nonn,tabf
AUTHOR
Seiichi Manyama, May 20 2018
STATUS
approved