A340247 Sum of the third largest parts r 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, 1, 1, 3, 5, 7, 10, 15, 19, 28, 33, 46, 57, 75, 84, 113, 129, 164, 184, 232, 256, 319, 347, 425, 466, 561, 601, 723, 777, 918, 981, 1152, 1224, 1428, 1509, 1746, 1849, 2122, 2227, 2550, 2678, 3040, 3184, 3600, 3760, 4234, 4410, 4942, 5151, 5745, 5961, 6635

Offset: 1

Author

Wesley Ivan Hurt, Jan 01 2021

Keywords

• nonn

Crossrefs

Cf. A062890, A340246, A340248, A340249.

Programs

Mathematica

Table[Sum[Sum[Sum[j*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))) * j.