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

20,4

Links

Alois P. Heinz, Table of n, a(n) for n = 20..10000

Index entries for sequences related to partitions

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

Example

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].

Prog

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

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.

Sequence in context: A134310 A308663 A305713 * A342518 A029041 A112582

Adjacent sequences: A259198 A259199 A259200 * A259202 A259203 A259204

Keyword

nonn,easy

Author

Doug Bell, Jun 20 2015

Status

approved