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A326637 Sum of the largest parts of the partitions of n into 10 squarefree parts. 11
0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 5, 13, 19, 34, 40, 60, 82, 126, 153, 219, 275, 385, 464, 621, 738, 996, 1168, 1514, 1780, 2287, 2643, 3302, 3839, 4743, 5456, 6638, 7605, 9225, 10479, 12512, 14199, 16929, 19061, 22453, 25300, 29690, 33283, 38715, 43333 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,12

LINKS

Table of n, a(n) for n=0..51.

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 * (n-i-j-k-l-m-o-p-q-r), where mu is the Möbius function (A008683).

a(n) = A326627(n) - A326628(n) - A326629(n) - A326630(n) - A326631(n) - A326632(n) - A326633(n) - A326634(n) - A326635(n) - A326636(n).

MATHEMATICA

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[(n-i-j-k-l-m-o-p-q-r) * 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, A326632, A326633, A326634, A326635, A326636.

Sequence in context: A308960 A326452 A326532 * A303355 A154692 A309161

Adjacent sequences:  A326634 A326635 A326636 * A326638 A326639 A326640

KEYWORD

nonn

AUTHOR

Wesley Ivan Hurt, Jul 14 2019

STATUS

approved

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Last modified June 17 19:57 EDT 2021. Contains 345085 sequences. (Running on oeis4.)