A309484 Sum of the squarefree parts of the partitions of n into 8 parts.

0, 0, 0, 0, 0, 0, 0, 0, 8, 9, 20, 29, 56, 83, 138, 193, 299, 408, 594, 789, 1115, 1462, 1977, 2551, 3382, 4279, 5550, 6948, 8856, 10970, 13742, 16841, 20832, 25303, 30892, 37180, 44972, 53652, 64276, 76108, 90424, 106352, 125353, 146501, 171544, 199318

Offset

0,9

Links

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

Index entries for sequences related to partitions

Formula

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

Mathematica

Table[Total[Select[Flatten[IntegerPartitions[n, {8}]], SquareFreeQ]], {n, 0, 50}] (* Harvey P. Dale, Jun 10 2021 *)

Crossrefs

Cf. A008683, A309461, A309478, A309479, A309480, A309481, A309482, A309484, A309485, A309486.

Sequence in context: A281225 A071869 A326444 * A308989 A048124 A322637

Adjacent sequences: A309481 A309482 A309483 * A309485 A309486 A309487

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 04 2019

Status

approved