A326473 Sum of the largest parts of the partitions of n into 9 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 2, 5, 9, 17, 27, 46, 69, 108, 158, 232, 326, 464, 633, 869, 1164, 1557, 2041, 2678, 3449, 4442, 5645, 7153, 8967, 11224, 13903, 17187, 21081, 25785, 31321, 37963, 45714, 54930, 65650, 78263, 92860, 109946, 129586, 152417, 178584

Offset: 0

Author

Wesley Ivan Hurt, Jul 10 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A026815, A326464, A326465, A326466, A326467, A326468, A326469, A326470, A326471, A326472.

Programs

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[(n-i-j-k-l-m-o-p-q), {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}]

Formula

a(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)} (n-i-j-k-l-m-o-p-q).

a(n) = A326464(n) - A326465(n) - A326466(n) - A326467(n) - A326468(n) - A326469(n) - A326470(n) - A326471(n) - A326472(n).