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A317084
Number of integer partitions of n whose multiplicities are weakly increasing and span an initial interval of positive integers.
2
1, 1, 1, 2, 2, 4, 4, 6, 7, 10, 11, 16, 17, 23, 27, 34, 38, 50, 54, 70, 79, 97, 107, 135, 148, 180, 205, 243, 270, 328, 360, 429, 480, 561, 625, 738, 810, 949, 1057, 1219, 1349, 1571, 1723, 1986, 2206, 2515, 2776, 3188, 3496, 3983, 4408, 4980, 5485, 6228, 6826
OFFSET
0,4
EXAMPLE
The a(7) = 6 integer partitions are (7), (61), (52), (43), (421), (331).
MATHEMATICA
normalQ[m_]:=Union[m]==Range[Max[m]];
Table[Length[Select[IntegerPartitions[n], And[normalQ[Length/@Split[#]], OrderedQ[Reverse[Length/@Split[#]]]]&]], {n, 60}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 21 2018
STATUS
approved