A308997 Sum of the second largest parts in the partitions of n into 8 parts.

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 3, 5, 10, 15, 27, 39, 63, 89, 133, 183, 264, 353, 488, 644, 864, 1116, 1465, 1863, 2397, 3009, 3802, 4713, 5877, 7200, 8859, 10753, 13084, 15731, 18956, 22603, 26993, 31948, 37839, 44477, 52307, 61082, 71349, 82842, 96177

Offset: 0

Author

Wesley Ivan Hurt, Jul 04 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A026814, A308989, A308990, A308991, A308992, A308994, A308995, A308996, A308998.

Programs

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[i, {i, j, Floor[(n - j - k - l - m - o - p)/2]}], {j, k, Floor[(n - k - l - m - o - p)/3]}], {k, l, Floor[(n - l - m - o - p)/4]}], {l, m, Floor[(n - m - o - p)/5]}], {m, o, Floor[(n - o - p)/6]}], {o, p, Floor[(n - p)/7]}], {p, Floor[n/8]}], {n, 0, 50}]
Table[Total[IntegerPartitions[n,{8}][[;;,2]]],{n,0,50}] (* Harvey P. Dale, Jun 22 2024 *)

Formula

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

a(n) = A308989(n) - A308990(n) - A308991(n) - A308992(n) - A308994(n) - A308995(n) - A308996(n) - A308998(n).