A259201 Number of partitions of n into ten primes.

1, 1, 1, 2, 2, 3, 4, 4, 5, 7, 8, 9, 11, 11, 14, 16, 18, 20, 25, 24, 31, 33, 38, 39, 48, 47, 59, 59, 69, 69, 87, 80, 102, 98, 118, 114, 143, 131, 168, 154, 191, 179, 227, 200, 261, 236, 297, 268, 344, 300, 396, 345, 442, 390, 509, 431, 576, 493, 641, 551, 729

Offset: 20

Author

Doug Bell, Jun 20 2015

Keywords

• nonn
• easy

Examples

			a(23) = 2 because there are 2 partitions of 23 into ten primes: [2,2,2,2,2,2,2,2,2,5] and [2,2,2,2,2,2,2,3,3,3].
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 20..10000
• Index entries for sequences related to partitions

Crossrefs

Column k=10 of A117278.

Number of partitions of n into r primes for r = 1-9: A010051, A061358, A068307, A259194, A259195, A259196, A259197, A259198, A259200.

Cf. A000040, A010051.

Programs

Magma

[#RestrictedPartitions(k,10,Set(PrimesUpTo(1000))):k in [20..80]] ; // Marius A. Burtea, Jul 13 2019

Formula

a(n) = [x^n y^10] Product_{k>=1} 1/(1 - y*x^prime(k)). - Ilya Gutkovskiy, Apr 18 2019

a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} A010051(r) * A010051(q) * A010051(p) * A010051(o) * A010051(m) * A010051(l) * A010051(k) * A010051(j) * A010051(i) * A010051(n-i-j-k-l-m-o-p-q-r). - Wesley Ivan Hurt, Jul 13 2019