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
Examples
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.
Links
- Alois P. Heinz, Table of n, a(n) for n = 0..1000
Programs
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Mathematica
A000041 = Table[PartitionsP[n], {n, 0, 45}]; Table[Length[Select[Flatten[IntegerPartitions[n]], MemberQ[A000041, #] &]], {n, 40}] (* Alonso del Arte, Aug 05 2011 *)