A326597 Sum of the second largest parts of the partitions of n into 10 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 5, 10, 15, 27, 39, 63, 91, 137, 190, 277, 376, 525, 704, 956, 1255, 1671, 2160, 2818, 3599, 4616, 5819, 7369, 9187, 11480, 14179, 17527, 21441, 26256, 31851, 38649, 46543, 56022, 66980, 80050, 95083, 112860, 133266

Offset

0,13

Links

Table of n, a(n) for n=0..49.

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)} i.

a(n) = A326588(n) - A326589(n) - A326590(n) - A326591(n) - A326592(n) - A326593(n) - A326594(n) - A326595(n) - A326596(n) - A326598(n).

Mathematica

Table[Total[IntegerPartitions[n, {10}][[;; , 2]]], {n, 0, 50}] (* Harvey P. Dale, Nov 19 2023 *)

Crossrefs

Cf. A026816, A326588, A326589, A326590, A326591, A326592, A326593, A326594, A326595, A326596, A326598.

Sequence in context: A308997 A045513 A326472 * A008337 A077285 A072523

Adjacent sequences: A326594 A326595 A326596 * A326598 A326599 A326600

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 13 2019

Status

approved