A309438 Number of prime parts in the partitions of n into 9 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 5, 11, 17, 30, 45, 72, 104, 147, 200, 279, 367, 491, 633, 825, 1042, 1330, 1649, 2063, 2531, 3116, 3776, 4597, 5510, 6627, 7878, 9381, 11058, 13059, 15275, 17895, 20802, 24191, 27942, 32303, 37099, 42628, 48719, 55678

Offset: 0

Author

Wesley Ivan Hurt, Aug 03 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A259200.

Programs

Mathematica

Table[Count[Flatten[IntegerPartitions[n,{9}]],?PrimeQ],{n,0,50}] (* _Harvey P. Dale, Jun 12 2021 *)

Formula

a(n) = Sum_{q=1..floor(n/9)} Sum_{p=q..floor((n-q)/8)} Sum_{o=p..floor((n-p-q)/7)} Sum_{m=o..floor((n-o-p-q)/6)} Sum_{l=m..floor((n-m-o-p-q)/5)} Sum_{k=l..floor((n-l-m-o-p-q)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q)/2)} (c(q) + c(p) + c(o) + c(m) + c(l) + c(k) + c(j) + c(i) + c(n-i-j-k-l-m-o-p-q)), where c = A010051.