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

0,13

Links

Table of n, a(n) for n=0..51.

Index entries for sequences related to partitions

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).

Mathematica

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

Crossrefs

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

Sequence in context: A308928 A308992 A326468 * A123569 A305651 A318185

Adjacent sequences: A326590 A326591 A326592 * A326594 A326595 A326596

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 13 2019

Status

approved