A377056 Antidiagonal-sums of the array A175804(n,k) = n-th term of k-th differences of partition numbers (A000041).

1, 1, 4, 3, 11, 2, 36, -27, 142, -207, 595, -1066, 2497, -4878, 10726, -22189, 48383, -103318, 224296, -480761, 1030299, -2186942, 4626313, -9740648, 20492711, -43109372, 90843475, -191769296, 405528200, -858373221, 1817311451, -3845483855, 8129033837

Offset

0,3

Links

Table of n, a(n) for n=0..32.

Example

Antidiagonal i + j = 3 of A175804 is (3, 1, 0, -1), so a(3) = 3.

Mathematica

nn=20;
t=Table[Differences[PartitionsP/@Range[0, 2nn], k], {k, 0, nn}];
Total/@Table[t[[j, i-j+1]], {i, nn}, {j, i}]

Crossrefs

For primes we have A140119 or A376683, unsigned A376681 or A376684.

These are the antidiagonal-sums of A175804.

First column of the same array is A281425.

For composites we have A377034, unsigned A377035.

For squarefree numbers we have A377039, unsigned A377040.

For nonsquarefree numbers we have A377049, unsigned A377048.

For prime powers we have A377052, unsigned A377053.

The unsigned version is A378621.

The version for strict partitions is A378970 (row-sums of A378622), unsigned A378971.

A000009 counts strict integer partitions, differences A087897, A378972.

A000041 counts integer partitions, differences A002865, A053445.

Cf. A008284, A047966, A075526, A116608, A225486, A293467, A325242, A325245, A325268, A377285.

Sequence in context: A222510 A100492 A072183 * A353341 A375035 A346614

Adjacent sequences: A377053 A377054 A377055 * A377057 A377058 A377059

Keyword

sign,new

Author

Gus Wiseman, Dec 12 2024

Status

approved