A326633 Sum of the fifth largest parts of the partitions of n into 10 squarefree parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 6, 10, 12, 18, 24, 36, 42, 58, 71, 97, 114, 149, 176, 230, 266, 338, 394, 498, 575, 714, 832, 1028, 1183, 1439, 1656, 2011, 2290, 2735, 3115, 3711, 4195, 4936, 5574, 6533, 7335, 8523, 9549, 11060, 12334, 14162

Offset

0,13

Links

Table of n, a(n) for n=0..54.

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 * l, where mu is the Möbius function (A008683).

a(n) = A326627(n) - A326628(n) - A326629(n) - A326630(n) - A326631(n) - A326632(n) - A326634(n) - A326635(n) - A326636(n) - A326637(n).

Mathematica

Table[Total[Select[IntegerPartitions[n, {10}], AllTrue[#, SquareFreeQ]&][[All, 5]]], {n, 0, 60}] (* Harvey P. Dale, Sep 29 2021 *)

Crossrefs

Cf. A008683, A326626, A326627, A326628, A326629, A326630, A326631, A326632, A326634, A326635, A326636, A326637.

Sequence in context: A309834 A326448 A326528 * A323587 A236634 A034406

Adjacent sequences: A326630 A326631 A326632 * A326634 A326635 A326636

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 14 2019

Status

approved