A326527 Sum of the sixth largest parts of the partitions of n into 9 squarefree parts.

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

Offset

0,12

Links

Table of n, a(n) for n=0..55.

Index entries for sequences related to partitions

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

Cf. A008683, A326522, A326523, A326524, A326525, A326526, A326528, A326529, A326530, A326531, A326532.

Sequence in context: A308955 A098386 A326447 * A326632 A240206 A229816

Adjacent sequences: A326524 A326525 A326526 * A326528 A326529 A326530

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 11 2019

Status

approved