A308991 - OEIS

%I #10 Apr 15 2022 09:19:52

%S 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,

%T 387,484,609,753,934,1142,1401,1695,2056,2468,2967,3532,4208,4974,

%U 5882,6904,8105,9458,11033,12798,14840,17124,19750,22674,26018,29735

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

%H <a href="/index/Par#part">Index entries for sequences related to partitions</a>

%F 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.

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

%t Table[Total[IntegerPartitions[n,{8}][[All,7]]],{n,0,60}] (* _Harvey P. Dale_, Apr 14 2022 *)

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

%K nonn

%O 0,11

%A _Wesley Ivan Hurt_, Jul 04 2019