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A317082
Number of integer partitions of n whose multiplicities are weakly decreasing and span an initial interval of positive integers.
3
1, 1, 1, 2, 3, 4, 5, 8, 9, 13, 17, 22, 26, 35, 42, 53, 66, 81, 96, 122, 143, 174, 210, 251, 293, 358, 417, 493, 582, 686, 793, 941, 1087, 1267, 1471, 1709, 1961, 2285, 2615, 3013, 3460, 3976, 4523, 5204, 5914, 6747, 7681, 8745, 9884, 11262, 12714, 14393, 16261
OFFSET
0,4
EXAMPLE
The a(7) = 8 integer partitions are (7), (61), (52), (511), (43), (421), (322), (3211).
MATHEMATICA
normalQ[m_]:=Union[m]==Range[Max[m]];
Table[Length[Select[IntegerPartitions[n], And[normalQ[Length/@Split[#]], OrderedQ[Length/@Split[#]]]&]], {n, 60}]
KEYWORD
nonn
AUTHOR
Gus Wiseman, Jul 21 2018
STATUS
approved