A286330 Number of partitions of n into a squarefree number of squarefree parts.

1, 1, 2, 3, 3, 5, 7, 10, 11, 15, 19, 26, 32, 42, 50, 66, 78, 101, 118, 150, 178, 224, 263, 327, 382, 471, 551, 670, 781, 944, 1098, 1317, 1526, 1821, 2105, 2498, 2879, 3399, 3908, 4592, 5266, 6164, 7056, 8220, 9388, 10897, 12424, 14368, 16342, 18843, 21394, 24585, 27858, 31932, 36119, 41277

Offset

0,3

Links

Table of n, a(n) for n=0..55.

Index entries for related partition-counting sequences

Example

a(8) = 11 because we have [7, 1], [6, 2], [6, 1, 1], [5, 3], [5, 2, 1], [3, 3, 2], [3, 2, 1, 1, 1], [3, 1, 1, 1, 1, 1], [2, 2, 2, 1, 1], [2, 2, 1, 1, 1, 1] and [2, 1, 1, 1, 1, 1, 1].

Mathematica

Join[{1}, Table[Length[Select[IntegerPartitions[n], SquareFreeQ[Length[#]] && AllTrue[#, SquareFreeQ] &]], {n, 55}]]

Crossrefs

Cf. A005117, A073576, A085755, A286141.

Sequence in context: A035553 A108961 A017984 * A241378 A226275 A035066

Adjacent sequences: A286327 A286328 A286329 * A286331 A286332 A286333

Keyword

nonn

Author

Ilya Gutkovskiy, May 07 2017

Status

approved