A308858 Sum of the second largest parts in the partitions of n into 5 primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 3, 5, 6, 8, 11, 11, 13, 20, 20, 27, 28, 35, 32, 51, 41, 60, 53, 74, 75, 112, 83, 136, 103, 162, 126, 205, 143, 246, 170, 283, 219, 365, 217, 415, 276, 475, 310, 554, 320, 642, 376, 690, 446, 835, 443, 944, 532, 1019, 587

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, A308857, A308859.

Programs

Mathematica

Table[Total[Select[IntegerPartitions[n,{5}],AllTrue[#,PrimeQ]&][[All,2]]],{n,0,60}] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 15 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) * i, where c = A010051.

a(n) = A308854(n) - A308855(n) - A308856(n) - A308857(n) - A308859(n).