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A317081 Number of integer partitions of n whose multiplicities span an initial interval of positive integers. 26
1, 1, 1, 2, 3, 5, 5, 9, 11, 16, 20, 30, 34, 50, 58, 79, 96, 129, 152, 203, 243, 307, 375, 474, 563, 707, 850, 1042, 1246, 1532, 1815, 2215, 2632, 3173, 3765, 4525, 5323, 6375, 7519, 8916, 10478, 12414, 14523, 17133, 20034, 23488, 27422, 32090, 37285, 43511, 50559 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Table of n, a(n) for n=0..50.

EXAMPLE

The a(7) = 9 integer partitions are (7), (61), (52), (511), (43), (421), (331), (322), (3211).

MATHEMATICA

normalQ[m_]:=Union[m]==Range[Max[m]];

Table[Length[Select[IntegerPartitions[n], normalQ[Length/@Split[#]]&]], {n, 30}]

CROSSREFS

Cf. A000041, A000837, A055932, A069799, A317082, A317084, A317085, A317087, A317090.

Sequence in context: A131319 A108962 A091608 * A183562 A222705 A241381

Adjacent sequences:  A317078 A317079 A317080 * A317082 A317083 A317084

KEYWORD

nonn

AUTHOR

Gus Wiseman, Jul 21 2018

STATUS

approved

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Last modified April 6 15:41 EDT 2020. Contains 333276 sequences. (Running on oeis4.)