A056870 Difference between partial sums of partition numbers (A026905) and partial sums of numbers of partitions into distinct parts (A026906).

0, 1, 2, 5, 9, 16, 26, 42, 64, 96, 140, 202, 285, 398, 547, 746, 1005, 1344, 1780, 2343, 3059, 3972, 5123, 6576, 8392, 10663, 13481, 16977, 21286, 26594, 33096, 41055, 50750, 62548, 76846, 94155, 115032, 140183, 170386, 206611, 249934, 301682

Offset: 1

Author

Robert G. Wilson v, Sep 02 2000

Keywords

• nonn

Crossrefs

Cf. A026905, A026906, A056871.

Programs

Mathematica

Table[ Sum[ PartitionsP[k], {k, 1, n}] - Sum[PartitionsQ[k], {k, 1, n}], {n, 1, 45}]
(* second program *)
Module[{nn=50},#[[1]]-#[[2]]&/@Thread[{Accumulate[PartitionsP[Range[nn]]],Accumulate[PartitionsQ[Range[nn]]]}]] (* Harvey P. Dale, Jun 19 2025 *)