A308996 Sum of the third largest parts in the partitions of n into 8 parts.

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 4, 7, 11, 19, 28, 44, 63, 92, 128, 183, 246, 337, 448, 597, 774, 1012, 1291, 1656, 2085, 2627, 3264, 4064, 4987, 6127, 7450, 9055, 10901, 13126, 15669, 18701, 22157, 26228, 30858, 36279, 42397, 49509, 57527, 66773, 77148

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, A308997, A308998.

Programs

Mathematica

Table[Total[IntegerPartitions[n,{8}][[All,3]]],{n,0,50}] (* Harvey P. Dale, Jul 19 2020 *)

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)} j.

a(n) = A308989(n) - A308990(n) - A308991(n) - A308992(n) - A308994(n) - A308995(n) - A308997(n) - A308998(n).