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A308990
Sum of the smallest parts in the partitions of n into 8 parts.
8
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 15, 23, 30, 42, 55, 75, 96, 127, 161, 209, 260, 330, 407, 509, 621, 765, 925, 1128, 1350, 1627, 1934, 2310, 2725, 3227, 3782, 4447, 5178, 6044, 7000, 8122, 9355, 10791, 12370, 14196, 16196, 18494, 21012, 23887
OFFSET
0,11
FORMULA
a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} p.
a(n) = A308989(n) - A308991(n) - A308992(n) - A308994(n) - A308995(n) - A308996(n) - A308997(n) - A308998(n).
MATHEMATICA
Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[p, {i, j, Floor[(n - j - k - l - m - o - p)/2]}], {j, k, Floor[(n - k - l - m - o - p)/3]}], {k, l, Floor[(n - l - m - o - p)/4]}], {l, m, Floor[(n - m - o - p)/5]}], {m, o, Floor[(n - o - p)/6]}], {o, p, Floor[(n - p)/7]}], {p, Floor[n/8]}], {n, 0, 50}]
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jul 04 2019
STATUS
approved