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A326632 Sum of the sixth largest parts of the partitions of n into 10 squarefree parts. 11
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 5, 9, 11, 16, 21, 31, 37, 51, 61, 83, 99, 129, 150, 197, 229, 288, 332, 417, 479, 589, 676, 830, 950, 1150, 1310, 1588, 1802, 2148, 2431, 2897, 3264, 3843, 4322, 5067, 5684, 6604, 7380, 8557, 9538, 10961, 12198 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,13
LINKS
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 * m, where mu is the Möbius function (A008683).
a(n) = A326627(n) - A326628(n) - A326629(n) - A326630(n) - A326631(n) - A326633(n) - A326634(n) - A326635(n) - A326636(n) - A326637(n).
MATHEMATICA
Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[m * MoebiusMu[r]^2 * MoebiusMu[q]^2 * MoebiusMu[p]^2 * MoebiusMu[o]^2 * MoebiusMu[m]^2 * MoebiusMu[l]^2 * MoebiusMu[k]^2 * MoebiusMu[j]^2 * MoebiusMu[i]^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
Sequence in context: A098386 A326447 A326527 * A240206 A229816 A099574
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jul 14 2019
STATUS
approved

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Last modified February 22 10:17 EST 2024. Contains 370250 sequences. (Running on oeis4.)