A309464 Number of squarefree parts in the partitions of n into 10 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 10, 20, 29, 49, 68, 106, 143, 209, 282, 394, 510, 692, 888, 1165, 1479, 1902, 2376, 3009, 3715, 4630, 5662, 6961, 8430, 10260, 12325, 14842, 17696, 21134, 25012, 29648, 34860, 41022, 47957, 56073, 65177, 75775, 87626, 101307

Offset

0,11

Links

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

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).

Mathematica

Table[Sum[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[r]^2 + MoebiusMu[n - i - j - k - l - m - o - p - q - r]^2), {i, j, Floor[(n - j - k - l - m - o - p - q - r)/2]}], {j, k, Floor[(n - k - l - m - o - p - q - r)/3]}], {k, l, Floor[(n - l - m - o - p - q - r)/4]}], {l, m, Floor[(n - m - o - p - q - r)/5]}], {m, o, Floor[(n - o - p - q - r)/6]}], {o, p, Floor[(n - p - q - r)/7]}], {p, q, Floor[(n - q - r)/8]}], {q, r, Floor[(n - r)/9]}], {r, Floor[n/10]}], {n, 0, 50}]

Crossrefs

Cf. A008683.

Sequence in context: A205724 A040091 A168461 * A368362 A022093 A332874

Adjacent sequences: A309461 A309462 A309463 * A309465 A309466 A309467

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 03 2019

Status

approved