A326590 Sum of the ninth 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, 11, 15, 22, 31, 44, 58, 80, 105, 140, 182, 238, 304, 393, 496, 630, 787, 986, 1219, 1512, 1853, 2273, 2765, 3362, 4055, 4894, 5860, 7016, 8351, 9931, 11746, 13885, 16330, 19188, 22452, 26242, 30549, 35531

Offset

0,13

Links

Table of n, a(n) for n=0..52.

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)} q.

a(n) = A326588(n) - A326589(n) - A326591(n) - A326592(n) - A326593(n) - A326594(n) - A326595(n) - A326596(n) - A326597(n) - A326598(n).

Mathematica

Table[Total[IntegerPartitions[n, {10}][[;; , 9]]], {n, 0, 60}] (* Harvey P. Dale, Mar 18 2023 *)

Crossrefs

Cf. A026816, A326588, A326589, A326591, A326592, A326593, A326594, A326595, A326596, A326597, A326598.

Sequence in context: A326465 A101977 A024793 * A116601 A218024 A236102

Adjacent sequences: A326587 A326588 A326589 * A326591 A326592 A326593

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 13 2019

Status

approved