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

0,17

Links

Table of n, a(n) for n=0..69.

Example

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, ...

Mathematica

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

Sequence in context: A029314 A071635 A156643 * A308626 A268755 A128664

Adjacent sequences: A378969 A378970 A378971 * A378973 A378974 A378975

Keyword

sign,new

Author

Gus Wiseman, Dec 14 2024

Status

approved