A309463 Number of squarefree parts in the partitions of n into 9 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 9, 18, 26, 44, 61, 95, 128, 187, 252, 343, 446, 600, 765, 995, 1256, 1600, 1987, 2493, 3053, 3772, 4583, 5582, 6712, 8103, 9657, 11534, 13649, 16165, 18987, 22324, 26041, 30401, 35269, 40899, 47174, 54414, 62432, 71612, 81791

Offset

0,10

Links

Table of n, a(n) for n=0..48.

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

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[(MoebiusMu[i]^2 + MoebiusMu[j]^2 + MoebiusMu[k]^2 + MoebiusMu[l]^2 + MoebiusMu[m]^2 + MoebiusMu[o]^2 + MoebiusMu[p]^2 + MoebiusMu[q]^2 + MoebiusMu[n - i - j - k - l - m - o - p - q]^2), {i, j, Floor[(n - j - k - l - m - o - p - q)/2]}], {j, k, Floor[(n - k - l - m - o - p - q)/3]}], {k, l, Floor[(n - l - m - o - p - q)/4]}], {l, m, Floor[(n - m - o - p - q)/5]}], {m, o, Floor[(n - o - p - q)/6]}], {o, p, Floor[(n - p - q)/7]}], {p, q, Floor[(n - q)/8]}], {q, Floor[n/9]}], {n, 0, 50}]

Crossrefs

Cf. A008683.

Sequence in context: A003886 A065999 A168419 * A242892 A112440 A022092

Adjacent sequences: A309460 A309461 A309462 * A309464 A309465 A309466

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 03 2019

Status

approved