A307637 Sum of the second largest parts of the partitions of n into 7 primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 3, 5, 6, 8, 14, 14, 16, 23, 28, 35, 38, 45, 52, 71, 66, 85, 94, 115, 121, 163, 154, 212, 194, 260, 253, 344, 289, 411, 382, 516, 457, 640, 533, 786, 652, 914, 778, 1112, 857, 1299, 1048, 1501, 1195, 1780, 1345

Offset: 0

Author

Wesley Ivan Hurt, Jul 04 2019

Keywords

• nonn

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A259197, A308974, A308975, A308976, A308977, A308978, A308979, A308980.

Programs

Mathematica

Table[Total[Select[IntegerPartitions[n,{7}],AllTrue[#,PrimeQ]&][[All,2]]],{n,0,60}] (* Harvey P. Dale, Oct 23 2022 *)

Formula

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

a(n) = A308974(n) - A308975(n) - A308976(n) - A308977(n) - A308978(n) - A308979(n) - A308980(n).