A340249 Sum of the largest parts t of the partitions of n into 4 parts q,r,s,t such that 1 <= q <= r <= s <= t and q + r + s > t.

0, 0, 0, 1, 2, 2, 5, 8, 14, 18, 30, 35, 56, 63, 95, 109, 156, 166, 235, 255, 346, 369, 491, 517, 676, 707, 907, 952, 1200, 1239, 1548, 1605, 1974, 2037, 2481, 2550, 3078, 3156, 3774, 3874, 4592, 4685, 5522, 5642, 6596, 6726, 7818, 7958, 9200, 9354, 10754, 10939, 12510

Offset: 1

Author

Wesley Ivan Hurt, Jan 01 2021

Keywords

• nonn

Crossrefs

Cf. A062890, A340246, A340247, A340248.

Programs

Mathematica

Table[Sum[Sum[Sum[(n - i - j - k) Sign[Floor[(i + k + j)/(n - i - j - k + 1)]], {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 60}]

Formula

a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} sign(floor((i+k+j)/(n-i-j-k+1))) * (n-i-j-k).