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A326527 Sum of the sixth largest parts of the partitions of n into 9 squarefree parts. 10
0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 5, 9, 11, 16, 21, 29, 35, 49, 57, 77, 91, 118, 137, 177, 202, 255, 293, 363, 413, 509, 580, 707, 802, 969, 1097, 1319, 1481, 1764, 1980, 2337, 2615, 3069, 3421, 3982, 4431, 5126, 5689, 6553, 7240, 8301, 9169, 10451 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,12
LINKS
FORMULA
a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} mu(q)^2 * mu(p)^2 * mu(o)^2 * mu(m)^2 * mu(l)^2 * mu(k)^2 * mu(j)^2 * mu(i)^2 * mu(n-i-j-k-l-m-o-p-q)^2 * m, where mu is the Möbius function (A008683).
a(n) = A326523(n) - A326524(n) - A326525(n) - A326526(n) - A326528(n) - A326529(n) - A326530(n) - A326531(n) - A326532(n).
MATHEMATICA
Table[Total[Select[IntegerPartitions[n, {9}], AllTrue[#, SquareFreeQ]&][[All, 6]]], {n, 0, 60}] (* Harvey P. Dale, Jul 05 2022 *)
CROSSREFS
Sequence in context: A308955 A098386 A326447 * A326632 A240206 A229816
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jul 11 2019
STATUS
approved

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Last modified March 1 14:57 EST 2024. Contains 370433 sequences. (Running on oeis4.)