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A326443 Number of partitions of n into 8 squarefree parts. 11
0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 2, 4, 5, 8, 9, 13, 15, 21, 24, 32, 36, 47, 53, 68, 75, 94, 105, 130, 143, 174, 192, 231, 254, 301, 330, 389, 424, 495, 539, 626, 678, 781, 847, 970, 1048, 1192, 1287, 1461, 1572, 1772, 1908, 2144, 2301, 2573, 2762, 3079, 3295 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,11

LINKS

Table of n, a(n) for n=0..57.

Index entries for sequences related to partitions

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, where mu is the Möbius function (A008683).

a(n) = A326444(n)/n for n > 0.

MATHEMATICA

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[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

Cf. A008683, A326444, A326445, A326446, A326447, A326448, A326449, A326450, A326451, A326452.

Sequence in context: A339560 A308952 A302401 * A326522 A326626 A341153

Adjacent sequences:  A326440 A326441 A326442 * A326444 A326445 A326446

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jul 06 2019

STATUS

approved

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Last modified September 29 12:57 EDT 2022. Contains 357090 sequences. (Running on oeis4.)