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

Author

Stefano Spezia, Aug 12 2023

Keywords

• nonn

Crossrefs

Cf. A000041, A325434, A364891.

Programs

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}]

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.