cp's OEIS Frontend

A308989 Sum of all the parts in the partitions of n into 8 parts.

%I A308989 #19 Jan 13 2022 11:41:54
%S A308989 0,0,0,0,0,0,0,0,8,9,20,33,60,91,154,225,352,493,720,988,1400,1869,
%T A308989 2552,3358,4464,5750,7488,9504,12152,15225,19140,23684,29408,35970,
%U A308989 44098,53445,64836,77848,93556,111423,132760,156948,185514,217838,255728,298350
%N A308989 Sum of all the parts in the partitions of n into 8 parts.
%H A308989 David A. Corneth, <a href="/A308989/b308989.txt">Table of n, a(n) for n = 0..10000</a> (first 101 terms from Harvey P. Dale)
%H A308989 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A308989 a(n) = 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)} 1.
%F A308989 a(n) = n * A026814(n).
%F A308989 a(n) = A308990(n) + A308991(n) + A308992(n) + A308994(n) + A308995(n) + A308996(n) + A308997(n) + A308998(n).
%t A308989 Table[Total[Flatten[IntegerPartitions[n,{8}]]],{n,0,50}] (* _Harvey P. Dale_, Jan 12 2022 *)
%Y A308989 Cf. A026814, A308990, A308991, A308992, A308994, A308995, A308996, A308997, A308998.
%K A308989 nonn,easy
%O A308989 0,9
%A A308989 _Wesley Ivan Hurt_, Jul 04 2019