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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 Table of n, a(n) for n=0..55. 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 * 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 Cf. A008683, A326626, A326627, A326628, A326629, A326630, A326631, A326633, A326634, A326635, A326636, A326637. Sequence in context: A098386 A326447 A326527 * A240206 A229816 A099574 Adjacent sequences: A326629 A326630 A326631 * A326633 A326634 A326635 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.)