A326468 Sum of the sixth largest parts of the partitions of n into 9 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 12, 17, 26, 37, 52, 71, 100, 133, 181, 239, 317, 410, 536, 682, 874, 1104, 1392, 1735, 2167, 2670, 3292, 4025, 4911, 5947, 7199, 8645, 10375, 12377, 14736, 17456, 20654, 24307, 28569, 33441, 39071, 45478, 52862

Offset

0,12

Links

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

Index entries for sequences related to partitions

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)} m.

a(n) = A326464(n) - A326465(n) - A326466(n) - A326467(n) - A326469(n) - A326470(n) - A326471(n) - A326472(n) - A326473(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[m, {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, A326464, A326465, A326466, A326467, A326469, A326470, A326471, A326472, A326473.

Sequence in context: A060730 A308928 A308992 * A326593 A123569 A305651

Adjacent sequences: A326465 A326466 A326467 * A326469 A326470 A326471

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 10 2019

Status

approved