A308857 Sum of the third largest parts in the partitions of n into 5 primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 5, 5, 8, 7, 9, 8, 16, 12, 21, 20, 27, 20, 41, 27, 46, 34, 54, 44, 78, 44, 86, 59, 104, 65, 129, 79, 152, 96, 175, 115, 221, 117, 249, 157, 295, 170, 342, 179, 394, 214, 430, 243, 517, 245, 584, 307, 643, 332, 730, 352

Offset: 0

Author

Wesley Ivan Hurt, Jun 28 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A259195, A308854, A308855, A308856, A308858, A308859.

Programs

Mathematica

Table[Total[Select[IntegerPartitions[n,{5}],AllTrue[#,PrimeQ]&][[All,3]]],{n,0,70}] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 06 2020 *)

Formula

a(n) = Sum_{l=1..floor(n/5)} Sum_{k=l..floor((n-l)/4)} Sum_{j=k..floor((n-k-l)/3)} Sum_{i=j..floor((n-j-k-l)/2)} c(l) * c(k) * c(j) * c(i) * c(n-i-j-k-l) * j, where c = A010051.

a(n) = A308854(n) - A308855(n) - A308856(n) - A308858(n) - A308859(n).