A308991 Sum of the seventh largest parts in the partitions of n into 8 parts.

0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 2, 3, 5, 7, 11, 16, 24, 32, 45, 60, 82, 107, 143, 184, 240, 303, 387, 484, 609, 753, 934, 1142, 1401, 1695, 2056, 2468, 2967, 3532, 4208, 4974, 5882, 6904, 8105, 9458, 11033, 12798, 14840, 17124, 19750, 22674, 26018, 29735

Offset: 0

Author

Wesley Ivan Hurt, Jul 04 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A026814, A308989, A308990, A308992, A308994, A308995, A308996, A308997, A308998.

Programs

Mathematica

Table[Total[IntegerPartitions[n,{8}][[All,7]]],{n,0,60}] (* Harvey P. Dale, Apr 14 2022 *)

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)} o.

a(n) = A308989(n) - A308990(n) - A308992(n) - A308994(n) - A308995(n) - A308996(n) - A308997(n) - A308998(n).