A309437 Number of prime parts in the partitions of n into 8 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 5, 11, 17, 30, 45, 72, 95, 138, 183, 253, 326, 433, 545, 706, 873, 1100, 1345, 1666, 2009, 2451, 2928, 3524, 4169, 4961, 5818, 6859, 7982, 9324, 10778, 12496, 14350, 16519, 18866, 21585, 24521, 27893, 31533, 35688, 40165

Offset: 0

Author

Wesley Ivan Hurt, Aug 03 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A259158, A309436.

Programs

Mathematica

Table[Count[Flatten[IntegerPartitions[n,{8}]],?PrimeQ],{n,0,50}] (* _Harvey P. Dale, May 21 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)} (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.