A326542 Sum of the eighth 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, 8, 8, 11, 15, 15, 19, 22, 24, 26, 34, 36, 44, 47, 53, 59, 73, 71, 87, 93, 109, 109, 138, 128, 163, 157, 190, 190, 238, 210, 277, 262, 325, 300, 387, 344, 457, 399, 515, 464, 617, 515

Offset

0,19

Links

Table of n, a(n) for n=0..64.

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) * p, where c = A010051.

a(n) = A326540(n) - A326541(n) - A326543(n) - A326544(n) - A326545(n) - A326546(n) - A326547(n) - A326548(n) - A326549(n).

Mathematica

Table[Total[Select[IntegerPartitions[n, {9}], AllTrue[#, PrimeQ]&][[All, 8]]], {n, 0, 70}] (* Harvey P. Dale, May 03 2022 *)

Crossrefs

Cf. A010051, A259200, A326540, A326541, A326543, A326544, A326545, A326546, A326547, A326548, A326549.

Sequence in context: A326541 A326680 A326456 * A326681 A308975 A326457

Adjacent sequences: A326539 A326540 A326541 * A326543 A326544 A326545

Keyword

nonn

Author

Wesley Ivan Hurt, Jul 13 2019

Status

approved