|
|
A259198
|
|
Number of partitions of n into eight primes.
|
|
20
|
|
|
1, 1, 1, 2, 2, 3, 4, 4, 5, 6, 7, 8, 10, 9, 12, 14, 16, 16, 21, 19, 26, 26, 31, 30, 39, 34, 46, 43, 53, 48, 65, 56, 77, 66, 85, 77, 104, 84, 118, 99, 133, 112, 155, 123, 177, 143, 196, 162, 227, 174, 256, 200, 282, 220, 318, 241, 360, 270, 389, 300, 442, 322
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
16,4
|
|
LINKS
|
|
|
FORMULA
|
a(n) = Sum_{p=1..floor(n/8)} Sum_{o=p..floor((n-p)/7)} Sum_{m=o..floor((n-o-p)/6)} Sum_{l=m..floor((n-m-o-p)/5)} Sum_{k=l..floor((n-l-m-o-p)/4)} Sum_{j=k..floor((n-k-l-m-o-p)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p)/2)} A010051(i) * A010051(j) * A010051(k) * A010051(l) * A010051(m) * A010051(o) * A010051(p) * A010051(n-i-j-k-l-m-o-p). - Wesley Ivan Hurt, Apr 17 2019
a(n) = [x^n y^8] Product_{k>=1} 1/(1 - y*x^prime(k)). - Ilya Gutkovskiy, Apr 18 2019
|
|
EXAMPLE
|
a(20) = 2 because there are 2 partitions of 20 into eight primes: [2,2,2,2,2,2,3,5] and [2,2,2,2,3,3,3,3].
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn,easy
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|