A326472 Sum of the second largest parts of the partitions of n into 9 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 5, 10, 15, 27, 39, 63, 91, 135, 188, 272, 368, 510, 682, 918, 1201, 1586, 2039, 2639, 3354, 4264, 5346, 6716, 8319, 10312, 12657, 15516, 18858, 22908, 27599, 33226, 39740, 47449, 56338, 66809, 78792, 92799, 108810, 127365

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, A326473.

Programs

Mathematica

Table[Total[IntegerPartitions[n,{9}][[;;,2]]],{n,0,50}] (* Harvey P. Dale, Dec 03 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)} i.

a(n) = A326464(n) - A326465(n) - A326466(n) - A326467(n) - A326468(n) - A326469(n) - A326470(n) - A326471(n) - A326473(n).