login
A340248
Sum of the second largest parts s of the partitions of n into 4 parts q,r,s,t such that 1 <= q <= r <= s <= t and q + r + s > t.
3
0, 0, 0, 1, 1, 2, 4, 7, 10, 15, 22, 29, 42, 51, 71, 87, 116, 132, 177, 201, 259, 289, 368, 404, 508, 550, 681, 738, 900, 959, 1164, 1239, 1482, 1569, 1863, 1962, 2313, 2424, 2835, 2971, 3448, 3590, 4150, 4318, 4954, 5142, 5872, 6080, 6912, 7140, 8078, 8343, 9395, 9672
OFFSET
1,6
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))) * i.
MATHEMATICA
Table[Sum[Sum[Sum[i*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}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jan 01 2021
STATUS
approved