A378972 Second differences of the strict partition numbers A000009.

0, 1, -1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 2, 0, 2, 2, 1, 2, 3, 2, 3, 4, 3, 4, 6, 4, 6, 8, 6, 9, 10, 9, 12, 14, 13, 16, 19, 18, 22, 26, 24, 30, 34, 34, 40, 45, 46, 53, 60, 62, 70, 79, 82, 93, 104, 108, 122, 136, 142, 160, 176, 186, 208, 228, 243, 268

Offset: 0

Author

Gus Wiseman, Dec 14 2024

Keywords

• sign

Examples

			The strict partition numbers begin (A000009):
  1, 1, 1, 2, 2, 3, 4, 5, 6, 8, 10, 12, 15, 18, 22, 27, 32, 38, ...
with differences (A087897 without first term):
  0, 0, 1, 0, 1, 1, 1, 1, 2, 2, 2, 3, 3, 4, 5, 5, 6, 8, 8, 10, 12, ...
with differences (a(n)):
  0, 1, -1, 1, 0, 0, 0, 1, 0, 0, 1, 0, 1, 1, 0, 1, 2, 0, 2, 2, 1, 2, ...
		

Crossrefs

For primes we have A036263.

The version for partitions is A053445.

For composites we have A073445.

For squarefree numbers we have A376590.

For nonsquarefree numbers we have A376593.

For powers of primes (inclusive) we have A376596.

For non powers of primes (inclusive) we have A376599.

Second row of A378622. See also:

- A293467 gives first column (up to sign).

- A377285 gives position of first zero in each row.

- A378970 gives row-sums.

- A378971 gives absolute value row-sums.

A000009 counts strict integer partitions, differences A087897, A378972.

A000041 counts integer partitions, differences A002865, A053445.

Cf. A047966, A098859, A225486, A325244, A325282.

Cf. A008284, A116608, A225485, A325242, A325268.

Programs

Mathematica

Differences[Table[PartitionsQ[n],{n,0,100}],2]