This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A309437 #11 May 15 2025 19:07:40
%S A309437 0,0,0,0,0,0,0,0,0,1,3,5,11,17,30,45,72,95,138,183,253,326,433,545,
%T A309437 706,873,1100,1345,1666,2009,2451,2928,3524,4169,4961,5818,6859,7982,
%U A309437 9324,10778,12496,14350,16519,18866,21585,24521,27893,31533,35688,40165
%N A309437 Number of prime parts in the partitions of n into 8 parts.
%H A309437 <a href="/index/Par#part">Index entries for sequences related to partitions</a>
%F A309437 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)} (c(i) + c(j) + c(k) + c(l) + c(m) + c(o) + c(p) + c(n-i-j-k-l-m-o-p)), where c = A010051.
%t A309437 Table[Count[Flatten[IntegerPartitions[n,{8}]],_?PrimeQ],{n,0,50}] (* _Harvey P. Dale_, May 21 2020 *)
%Y A309437 Cf. A010051, A259158, A309436.
%K A309437 nonn
%O A309437 0,11
%A A309437 _Wesley Ivan Hurt_, Aug 03 2019