A308995 Sum of the fourth largest parts in the partitions of n into 8 parts.

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 6, 9, 15, 22, 35, 48, 71, 97, 139, 185, 254, 334, 447, 575, 752, 955, 1227, 1537, 1939, 2401, 2991, 3661, 4500, 5458, 6639, 7977, 9607, 11452, 13673, 16176, 19154, 22511, 26470, 30906, 36096, 41906, 48652, 56171, 64847

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, A308996, A308997, A308998.

Programs

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[k, {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}][[;;,4]]],{n,0,60}] (* Harvey P. Dale, Nov 20 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)} k.

a(n) = A308989(n) - A308990(n) - A308991(n) - A308992(n) - A308994(n) - A308996(n) - A308997(n) - A308998(n).