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A309464 Number of squarefree parts in the partitions of n into 10 parts. 1
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 (list; graph; refs; listen; history; text; internal format)
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 * A022093 A332874 A076817

Adjacent sequences:  A309461 A309462 A309463 * A309465 A309466 A309467

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Aug 03 2019

STATUS

approved

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Last modified September 24 22:33 EDT 2021. Contains 347651 sequences. (Running on oeis4.)