A326526 Sum of the seventh 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, 8, 10, 15, 19, 26, 31, 43, 51, 67, 78, 103, 119, 152, 172, 219, 250, 308, 348, 429, 486, 585, 658, 794, 892, 1063, 1185, 1410, 1572, 1847, 2053, 2407, 2670, 3095, 3425, 3964, 4380, 5030, 5532, 6344, 6974, 7939

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

a(n) = A326523(n) - A326524(n) - A326525(n) - A326527(n) - A326528(n) - A326529(n) - A326530(n) - A326531(n) - A326532(n).

Mathematica

Table[Total[Select[IntegerPartitions[n, {9}], AllTrue[#, SquareFreeQ]&][[All, 7]]], {n, 0, 60}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Dec 05 2020 *)

Crossrefs

Cf. A008683, A326522, A326523, A326524, A326525, A326527, A326528, A326529, A326530, A326531, A326532.

Sequence in context: A271593 A131945 A240308 * A035951 A035957 A035964

Adjacent sequences: A326523 A326524 A326525 * A326527 A326528 A326529

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 11 2019

Status

approved