A326630 Sum of the eighth largest parts in the partitions of n into 10 squarefree parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 5, 8, 9, 14, 18, 26, 30, 41, 50, 66, 77, 100, 117, 152, 174, 219, 252, 314, 357, 436, 499, 605, 685, 820, 929, 1109, 1243, 1469, 1650, 1947, 2169, 2536, 2833, 3297, 3663, 4235, 4707, 5424, 6000, 6867, 7604, 8684

Offset

0,13

Links

Table of n, a(n) for n=0..56.

Index entries for sequences related to partitions

Formula

a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} mu(r)^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-r)^2 * p, where mu is the Möbius function (A008683).

a(n) = A326627(n) - A326628(n) - A326629(n) - A326631(n) - A326632(n) - A326633(n) - A326634(n) - A326635(n) - A326636(n) - A326637(n).

Mathematica

Table[Select[IntegerPartitions[n, {10}], AllTrue[#, SquareFreeQ]&][[All, 8]]//Total, {n, 0, 60}] (* Harvey P. Dale, Apr 19 2020 *)

Crossrefs

Cf. A008683, A005117, A326626, A326627, A326628, A326629, A326631, A326632, A326633, A326634, A326635, A326636, A326637.

Sequence in context: A183564 A222707 A326525 * A317810 A308954 A053097

Adjacent sequences: A326627 A326628 A326629 * A326631 A326632 A326633

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 14 2019

Status

approved