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A326447 Sum of the sixth largest parts in the partitions of n into 8 squarefree parts. 9
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 5, 9, 11, 16, 19, 27, 33, 45, 51, 69, 80, 105, 117, 150, 172, 216, 242, 300, 339, 416, 466, 568, 636, 768, 852, 1022, 1135, 1348, 1483, 1748, 1934, 2260, 2481, 2876, 3163, 3655, 3993, 4582, 5014, 5735, 6244, 7098, 7732 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,11
LINKS
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(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)^2 * m, where mu is the Möbius function (A008683).
a(n) = A326444(n) - A326445(n) - A326446(n) - A326448(n) - A326449(n) - A326450(n) - A326451(n) - A326452(n).
MATHEMATICA
Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[m * 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]^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
Sequence in context: A050045 A308955 A098386 * A326527 A326632 A240206
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jul 06 2019
STATUS
approved

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Last modified February 28 06:43 EST 2024. Contains 370387 sequences. (Running on oeis4.)