A326544 Sum of the sixth largest parts of the partitions of n into 9 primes.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2, 2, 2, 4, 4, 6, 9, 9, 12, 16, 17, 21, 24, 26, 30, 38, 41, 49, 56, 62, 71, 88, 88, 107, 114, 133, 138, 173, 162, 206, 205, 247, 246, 311, 282, 372, 352, 438, 404, 527, 469, 624, 553, 716, 641, 862, 731

Offset: 0

Author

Wesley Ivan Hurt, Jul 13 2019

Keywords

• nonn
• changed

Links

• Index entries for sequences related to partitions

Crossrefs

Cf. A010051, A259200, A326540, A326541, A326542, A326543, A326545, A326546, A326547, A326548, A326549.

Programs

Mathematica

Table[Total[Select[IntegerPartitions[n,{9}],AllTrue[#,PrimeQ]&][[All,6]]],{n,0,70}] (* Harvey P. Dale, Jan 01 2023 *)

Formula

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

a(n) = A326540(n) - A326541(n) - A326542(n) - A326543(n) - A326545(n) - A326546(n) - A326547(n) - A326548(n) - A326549(n).