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

1,3

Links

Table of n, a(n) for n=1..42.

Mathematica

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

Crossrefs

Cf. A026905, A026906, A056871.

Sequence in context: A362548 A225596 A211881 * A326507 A014739 A290464

Adjacent sequences: A056867 A056868 A056869 * A056871 A056872 A056873

Keyword

nonn

Author

Robert G. Wilson v, Sep 02 2000

Status

approved