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A308907
Sum of the fifth largest parts in the partitions of n into 6 squarefree parts.
7
0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 6, 10, 10, 14, 18, 26, 28, 37, 41, 57, 62, 77, 87, 113, 122, 152, 170, 213, 230, 279, 307, 376, 402, 471, 516, 622, 661, 768, 830, 978, 1041, 1194, 1282, 1492, 1586, 1804, 1932, 2217, 2340, 2632, 2815, 3195, 3380, 3780, 4026
OFFSET
0,9
FORMULA
a(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)} mu(m)^2 * mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-k-j-l-m)^2 * l, where mu is the Möbius function (A008683).
a(n) = A308903(n) - A308906(n) - A308908(n) - A308909(n) - A308910(n) - A308911(n).
MATHEMATICA
Table[Sum[Sum[Sum[Sum[Sum[l*MoebiusMu[i]^2*MoebiusMu[j]^2*MoebiusMu[k]^2* MoebiusMu[l]^2*MoebiusMu[m]^2*MoebiusMu[n - i - j - k - l - m]^2, {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, 50}]
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 29 2019
STATUS
approved