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

0,4

Links

Table of n, a(n) for n=0..52.

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}]

Crossrefs

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

Sequence in context: A342094 A094103 A349412 * A268359 A329203 A054181

Adjacent sequences: A317079 A317080 A317081 * A317083 A317084 A317085

Keyword

nonn

Author

Gus Wiseman, Jul 21 2018

Status

approved