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
Keywords
Programs
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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 *)