A326546 Sum of the fourth largest parts in 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, 5, 7, 10, 10, 14, 18, 19, 23, 30, 32, 38, 49, 54, 65, 74, 83, 97, 120, 118, 148, 159, 189, 193, 242, 231, 299, 293, 359, 357, 454, 407, 543, 517, 649, 600, 788, 706, 952, 851, 1102, 1004, 1351

Offset

0,19

Links

Table of n, a(n) for n=0..63.

Index entries for sequences related to partitions

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) * k, where c is the prime characteristic (A010051).

a(n) = A326540(n) - A326541(n) - A326542(n) - A326543(n) - A326544(n) - A326545(n) - A326547(n) - A326548(n) - A326549(n).

Mathematica

Table[Total[Select[IntegerPartitions[n, {9}], AllTrue[#, PrimeQ]&][[;; , 4]]], {n, 0, 70}] (* Harvey P. Dale, Mar 09 2023 *)

Crossrefs

Cf. A010051, A259200, A326540, A326541, A326542, A326543, A326544, A326545, A326547, A326548, A326549.

Sequence in context: A308922 A308978 A326460 * A326685 A274150 A057591

Adjacent sequences: A326543 A326544 A326545 * A326547 A326548 A326549

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 13 2019

Status

approved