VOOZH about

URL: https://oeis.org/A308857

⇱ A308857 - OEIS

login
A308857
Sum of the third largest parts in the partitions of n into 5 primes.
5
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
0,11
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).
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 *)
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Jun 28 2019
STATUS
approved