A326469 Sum of the fifth largest parts of the partitions of n into 9 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 8, 13, 19, 29, 42, 60, 83, 117, 158, 216, 288, 383, 500, 655, 840, 1080, 1371, 1734, 2172, 2718, 3364, 4157, 5099, 6235, 7574, 9184, 11059, 13294, 15895, 18955, 22501, 26657, 31432, 36991, 43368, 50731, 59138, 68811

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)} l.

a(n) = A326464(n) - A326465(n) - A326466(n) - A326467(n) - A326468(n) - A326470(n) - A326471(n) - A326472(n) - A326473(n).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[l, {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}]
Table[Total[IntegerPartitions[n, {9}][[All, -5]]], {n, 0, 60}] (* Harvey P. Dale, Nov 07 2020 *)

Crossrefs

Cf. A026815, A326464, A326465, A326466, A326467, A326468, A326470, A326471, A326472, A326473.

Sequence in context: A178741 A308929 A308994 * A326594 A045842 A324741

Adjacent sequences: A326466 A326467 A326468 * A326470 A326471 A326472

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 10 2019

Status

approved