A183088 Total number of parts that are partition numbers A000041 in all partitions of n.

0, 1, 3, 6, 11, 19, 32, 50, 77, 115, 170, 244, 348, 485, 674, 922, 1251, 1678, 2241, 2959, 3892, 5076, 6592, 8497, 10915, 13930, 17719, 22417, 28267, 35474, 44395, 55312, 68730, 85082, 105049, 129261, 158675, 194171, 237077, 288651

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..1000

Example

a(5) = 19 because the 7 partitions of 5 are [5], [4, 1], [3, 2], [3, 1, 1], [2, 2, 1], [2, 1, 1, 1], [1, 1, 1, 1, 1] and we can see that there are 19 parts that are partition numbers A000041. Note that there are 20 parts but the 4 is not a partition number, so a(5) = 20 - 1 = 19.

Mathematica

A000041 = Table[PartitionsP[n], {n, 0, 45}]; Table[Length[Select[Flatten[IntegerPartitions[n]], MemberQ[A000041, #] &]], {n, 40}] (* Alonso del Arte, Aug 05 2011 *)

Crossrefs

Cf. A006128, A037032, A144115.

Sequence in context: A114089 A001976 A144115 * A326957 A116557 A001911

Adjacent sequences: A183085 A183086 A183087 * A183089 A183090 A183091

Keyword

nonn,less

Author

Omar E. Pol, Aug 05 2011

Status

approved