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A308867
Sum of all the parts in the partitions of n into 6 parts.
6
0, 0, 0, 0, 0, 0, 6, 7, 16, 27, 50, 77, 132, 182, 280, 390, 560, 748, 1044, 1349, 1800, 2310, 2992, 3749, 4776, 5875, 7332, 8937, 10948, 13166, 15960, 18972, 22688, 26763, 31654, 36995, 43416, 50320, 58520, 67431, 77800, 89052, 102144, 116186, 132396, 149895
OFFSET
0,7
FORMULA
a(n) = n * Sum_{m=1..floor(n/6)} Sum_{l=m..floor((n-m)/5)} Sum_{k=l..floor((n-l-m)/4)} Sum_{j=k..floor((n-k-l-m)/3)} Sum_{i=j..floor((n-j-k-l-m)/2)} 1.
a(n) = n * A238340(n).
a(n) = A308868(n) + A308869(n) + A306670(n) + A306671(n) + A308872(n) + A308873(n).
MATHEMATICA
Table[n*Sum[Sum[Sum[Sum[Sum[1, {i, j, Floor[(n - j - k - l - m)/2]}], {j, k, Floor[(n - k - l - m)/3]}], {k, l, Floor[(n - l - m)/4]}], {l, m, Floor[(n - m)/5]}], {m, Floor[n/6]}], {n, 0, 100}]
Table[Total[Flatten[IntegerPartitions[n, {6}]]], {n, 0, 50}] (* Harvey P. Dale, Oct 29 2024 *)
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 29 2019
STATUS
approved