A317084 Number of integer partitions of n whose multiplicities are weakly increasing and span an initial interval of positive integers.

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

Author

Gus Wiseman, Jul 21 2018

Keywords

• nonn

Examples

			The a(7) = 6 integer partitions are (7), (61), (52), (43), (421), (331).
		

Crossrefs

Cf. A000041, A000837, A055932, A242031, A317081, A317082, A317085, A317087, A317090.

Programs

Mathematica

normalQ[m_]:=Union[m]==Range[Max[m]];
Table[Length[Select[IntegerPartitions[n],And[normalQ[Length/@Split[#]],OrderedQ[Reverse[Length/@Split[#]]]]&]],{n,60}]