A326626 Number of 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, 13, 16, 23, 26, 35, 41, 54, 62, 79, 90, 115, 130, 161, 182, 224, 251, 303, 341, 408, 456, 539, 601, 709, 786, 915, 1014, 1179, 1299, 1496, 1649, 1892, 2078, 2368, 2597, 2953, 3230, 3645, 3986, 4492, 4895

Offset

0,13

Links

David A. Corneth, Table of n, a(n) for n = 0..9999

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, where mu is the Möbius function (A008683).

a(n) = A326627(n)/n for n > 0.

Mathematica

Table[Count[IntegerPartitions[n, {10}], _?(AllTrue[#, SquareFreeQ]&)], {n, 0, 60}] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Aug 25 2019 *)

Crossrefs

Cf. A008683, A326627, A326628, A326629, A326630, A326631, A326632, A326633, A326634, A326635, A326636, A326637.

Sequence in context: A302401 A326443 A326522 * A341153 A326628 A326524

Adjacent sequences: A326623 A326624 A326625 * A326627 A326628 A326629

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 14 2019

Status

approved