A326465 Sum of the smallest parts of the partitions of n into 9 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 15, 22, 31, 42, 56, 76, 99, 130, 168, 216, 274, 349, 435, 544, 674, 831, 1017, 1244, 1507, 1823, 2194, 2629, 3136, 3734, 4420, 5223, 6148, 7215, 8438, 9851, 11453, 13292, 15382, 17758, 20447, 23502, 26935

Offset: 0

Author

Wesley Ivan Hurt, Jul 07 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A026815, A326464, A326466, A326467, A326468, A326469, A326470, A326471, A326472, A326473.

Programs

Mathematica

Table[Total[Last/@IntegerPartitions[n,{9}]],{n,0,60}] (* Harvey P. Dale, Sep 13 2019 *)

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)} q.

a(n) = A326464(n) - A326466(n) - A326467(n) - A326468(n) - A326469(n) - A326470(n) - A326471(n) - A326472(n) - A326473(n).