A309461 Number of squarefree parts in the partitions of n into 8 parts.

0, 0, 0, 0, 0, 0, 0, 0, 8, 8, 16, 23, 39, 54, 84, 113, 165, 214, 294, 377, 504, 634, 820, 1020, 1292, 1581, 1966, 2382, 2920, 3502, 4233, 5033, 6021, 7098, 8404, 9835, 11548, 13416, 15631, 18046, 20879, 23965, 27545, 31451, 35949, 40838, 46426, 52504, 59406

Offset

0,9

Links

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

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)} (mu(i)^2 + mu(j)^2 + mu(k)^2 + mu(l)^2 + mu(m)^2 + mu(o)^2 + mu(p)^2 + mu(n-i-j-k-l-m-o-p)^2), where mu is the Möbius function (A008683).

Mathematica

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

Crossrefs

Cf. A008683.

Sequence in context: A168397 A186986 A112439 * A245420 A022091 A171188

Adjacent sequences: A309458 A309459 A309460 * A309462 A309463 A309464

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 03 2019

Status

approved