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

0,4

Links

Table of n, a(n) for n=0..54.

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}]

Crossrefs

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

Sequence in context: A357456 A185224 A001996 * A122134 A035940 A067772

Adjacent sequences: A317081 A317082 A317083 * A317085 A317086 A317087

Keyword

nonn

Author

Gus Wiseman, Jul 21 2018

Status

approved