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A308769
Sum of the second largest parts of the partitions of n into 4 squarefree parts.
4
0, 0, 0, 0, 1, 1, 3, 4, 8, 8, 14, 15, 24, 25, 41, 45, 64, 64, 85, 93, 120, 123, 159, 172, 221, 222, 279, 291, 375, 386, 472, 494, 610, 612, 734, 745, 901, 899, 1075, 1067, 1297, 1272, 1493, 1490, 1765, 1757, 2046, 2076, 2398, 2408, 2743, 2774, 3187, 3177
OFFSET
0,7
FORMULA
a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-j-k)^2 * i, where mu(n) is the Möbius function (A008683).
a(n) = A308783(n) - A308768(n) - A308762(n) - A308770(n).
MATHEMATICA
Table[Sum[Sum[Sum[i * MoebiusMu[k]^2*MoebiusMu[j]^2*MoebiusMu[i]^2* MoebiusMu[n - i - j - k]^2, {i, j, Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 0, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 23 2019
STATUS
approved