A309439 Number of prime parts in the partitions of n into 10 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 3, 5, 11, 17, 30, 45, 72, 104, 157, 210, 298, 396, 537, 698, 924, 1176, 1521, 1909, 2418, 2991, 3729, 4560, 5610, 6795, 8254, 9906, 11919, 14180, 16908, 19972, 23615, 27706, 32527, 37917, 44227, 51267, 59425, 68525, 79007

Offset: 0

Author

Wesley Ivan Hurt, Aug 03 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A259201.

Programs

Mathematica

Table[Count[Flatten[IntegerPartitions[n,{10}]],?PrimeQ],{n,0,50}] (* _Harvey P. Dale, Dec 26 2020 *)

Formula

a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} (c(r) + 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-r)), where c = A010051.