A364892 Row sums of A364891.

0, 0, 1, 1, 2, 2, 4, 5, 8, 10, 15, 19, 27, 34, 47, 59, 79, 99, 130, 162, 210, 260, 332, 410, 517, 635, 794, 970, 1202, 1463, 1799, 2180, 2664, 3214, 3904, 4693, 5669, 6789, 8163, 9740, 11658, 13865, 16527, 19592, 23267, 27496, 32538, 38343, 45223, 53142, 62488

Offset

1,5

Links

Table of n, a(n) for n=1..51.

Formula

a(n) = Sum_{k=1..n} ((-1)^(k-1)*Sum_{j=0..k-1} (-1)^j*(p(n - j*(2*j + 1)) - p(n - (j + 1)*(2*j + 1)))), where p(n) = A000041(n) is the number of partitions of n.

Conjecture: lim_{n->oo} a(n)/A000041(n) = 1/4.

Mathematica

A364891[n_, k_]:=(-1)^(k-1)*Sum[(-1)^j*(PartitionsP[n-j(2j+1)]-PartitionsP[n-(j+1)(2j+1)]), {j, 0, k-1}]; Table[Sum[A364891[n, k], {k, 1, n}], {n, 1, 51}]

Crossrefs

Cf. A000041, A325434, A364891.

Sequence in context: A036002 A104504 A027337 * A325434 A326631 A260894

Adjacent sequences: A364889 A364890 A364891 * A364893 A364894 A364895

Keyword

nonn

Author

Stefano Spezia, Aug 12 2023

Status

approved