A326593 Sum of the sixth largest parts of the partitions of n into 10 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 12, 17, 26, 37, 54, 73, 104, 139, 191, 253, 340, 442, 584, 749, 970, 1232, 1571, 1971, 2486, 3087, 3844, 4734, 5835, 7119, 8699, 10530, 12753, 15332, 18426, 21998, 26259, 31153, 36938, 43575, 51360, 60250

Offset: 0

Author

Wesley Ivan Hurt, Jul 13 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A026816, A326588, A326589, A326590, A326591, A326592, A326594, A326595, A326596, A326597, A326598.

Programs

Mathematica

Table[Total[IntegerPartitions[n,{10}][[All,6]]],{n,0,60}] (* Harvey P. Dale, Dec 20 2020 *)

Formula

a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} m.

a(n) = A326588(n) - A326589(n) - A326590(n) - A326591(n) - A326592(n) - A326594(n) - A326595(n) - A326596(n) - A326597(n) - A326598(n).