A317082 Number of integer partitions of n whose multiplicities are weakly decreasing and span an initial interval of positive integers.

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

Author

Gus Wiseman, Jul 21 2018

Keywords

• nonn

Examples

			The a(7) = 8 integer partitions are (7), (61), (52), (511), (43), (421), (322), (3211).
		

Crossrefs

Cf. A000041, A000837, A055932, A304678, A317081, A317084, A317085, A317087, A317090.

Programs

Mathematica

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