A326470 Sum of the fourth largest parts of the partitions of n into 9 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 6, 9, 15, 22, 35, 50, 73, 101, 145, 196, 270, 360, 484, 632, 832, 1069, 1382, 1755, 2229, 2794, 3508, 4346, 5384, 6608, 8101, 9847, 11960, 14413, 17354, 20760, 24791, 29444, 34923, 41201, 48535, 56926, 66654, 77731

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, A326471, A326472, A326473.

Programs

Mathematica

Table[Total[IntegerPartitions[n,{9}][[;;,4]]],{n,0,50}] (* Harvey P. Dale, May 01 2023 *)

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)} k.

a(n) = A326464(n) - A326465(n) - A326466(n) - A326467(n) - A326468(n) - A326469(n) - A326471(n) - A326472(n) - A326473(n).