A378971 Antidiagonal-sums of absolute value of the array A378622(n,k) = n-th term of k-th differences of strict partition numbers (A000009).

1, 1, 1, 5, 8, 18, 30, 47, 70, 110, 177, 309, 574, 1063, 1892, 3107, 4598, 6166, 8737, 20603, 62457, 149132, 314116, 614093, 1155968, 2176048, 4244322, 8753864, 19006756, 42472117, 95235017, 210396059, 453414950, 949510166, 1931941261, 3826650257, 7400745917

Offset

0,4

Links

Table of n, a(n) for n=0..36.

Example

Antidiagonal 4 of A378622 is (2, 0, -1, -2, -3), so a(4) = 8.

Mathematica

nn=30;
t=Table[Take[Differences[PartitionsQ/@Range[0, 2nn], k], nn], {k, 0, nn}];
Total/@Abs/@Table[t[[j, i-j+1]], {i, nn/2}, {j, i}]

Crossrefs

For primes we have A376681 or A376684, signed version A140119 or A376683.

For composites we have A377035, signed version A377034.

For squarefree numbers we have A377040, signed version A377039.

For nonsquarefree numbers we have A377048, signed version A377049.

For prime powers we have A377053, signed version A377052.

For partition numbers we have A378621, signed version A377056.

Row-sums of the triangular form of A378622. See also:

- A175804 is the version for partitions.

- A293467 gives the first column (up to sign).

- A377285 gives position of first zero in each row.

The signed version is A378970.

A000009 counts strict integer partitions, differences A087897, A378972.

A000041 counts integer partitions, differences A002865, A053445.

Cf. A008284, A047966, A098859, A116608, A225486, A325242, A325244, A325245, A325268.

Sequence in context: A219049 A245534 A302393 * A342804 A226902 A347136

Adjacent sequences: A378968 A378969 A378970 * A378972 A378973 A378974

Keyword

nonn,new

Author

Gus Wiseman, Dec 14 2024

Status

approved