A326464 Sum of all the parts in the partitions of n into 9 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 9, 10, 22, 36, 65, 98, 165, 240, 374, 540, 779, 1080, 1533, 2068, 2829, 3768, 5025, 6552, 8586, 11004, 14152, 17940, 22692, 28384, 35508, 43894, 54215, 66420, 81178, 98496, 119340, 143560, 172446, 205968, 245444, 291060, 344565

Offset

0,10

Links

Table of n, a(n) for n=0..45.

Index entries for sequences related to partitions

Formula

a(n) = n * Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} 1.

a(n) = A326465(n) + A326466(n) + A326467(n) + A326468(n) + A326469(n) + A326470(n) + A326471(n) + A326472(n) + A326473(n).

Mathematica

Table[n * Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[1, {i, j, Floor[(n - j - k - l - m - o - p - q)/2]}], {j, k, Floor[(n - k - l - m - o - p - q)/3]}], {k, l, Floor[(n - l - m - o - p - q)/4]}], {l, m, Floor[(n - m - o - p - q)/5]}], {m, o, Floor[(n - o - p - q)/6]}], {o, p, Floor[(n - p - q)/7]}], {p, q, Floor[(n - q)/8]}], {q, Floor[n/9]}], {n, 0, 50}]

Crossrefs

Cf. A026815, A326465, A326466, A326467, A326468, A326469, A326470, A326471, A326472, A326473.

Sequence in context: A061410 A309485 A228378 * A174042 A263261 A290275

Adjacent sequences: A326461 A326462 A326463 * A326465 A326466 A326467

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 07 2019

Status

approved