The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A326633 Sum of the fifth 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, 6, 10, 12, 18, 24, 36, 42, 58, 71, 97, 114, 149, 176, 230, 266, 338, 394, 498, 575, 714, 832, 1028, 1183, 1439, 1656, 2011, 2290, 2735, 3115, 3711, 4195, 4936, 5574, 6533, 7335, 8523, 9549, 11060, 12334, 14162 (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 * l, where mu is the Möbius function (A008683). a(n) = A326627(n) - A326628(n) - A326629(n) - A326630(n) - A326631(n) - A326632(n) - A326634(n) - A326635(n) - A326636(n) - A326637(n). MATHEMATICA Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[l * 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, A326634, A326635, A326636, A326637. Sequence in context: A309834 A326448 A326528 * A323587 A236634 A034406 Adjacent sequences:  A326630 A326631 A326632 * A326634 A326635 A326636 KEYWORD nonn AUTHOR Wesley Ivan Hurt, Jul 14 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified October 22 19:55 EDT 2020. Contains 337954 sequences. (Running on oeis4.)