A259197 Number of partitions of n into seven primes.

1, 1, 1, 2, 2, 3, 4, 4, 4, 6, 6, 8, 8, 9, 10, 14, 12, 16, 16, 19, 19, 26, 22, 30, 26, 34, 31, 43, 33, 48, 42, 56, 47, 66, 51, 77, 60, 84, 68, 99, 73, 112, 86, 123, 95, 143, 103, 162, 116, 174, 131, 200, 137, 220, 156, 241, 171, 270, 180, 300, 202, 322, 223, 359

Offset

14,4

Links

Alois P. Heinz, Table of n, a(n) for n = 14..10000

Index entries for sequences related to partitions

Formula

a(n) = Sum_{o=1..floor(n/7)} Sum_{m=o..floor((n-o)/6)} Sum_{l=m..floor((n-m-o)/5)} Sum_{k=l..floor((n-l-m-o)/4)} Sum_{j=k..floor((n-k-l-m-o)/3)} Sum_{i=j..floor((n-j-k-l-m-o)/2)} A010051(i) * A010051(j) * A010051(k) * A010051(l) * A010051(m) * A010051(o) * A010051(n-i-j-k-l-m-o). - Wesley Ivan Hurt, Apr 17 2019

a(n) = [x^n y^7] Product_{k>=1} 1/(1 - y*x^prime(k)). - Ilya Gutkovskiy, Apr 18 2019

Example

a(17) = 2 because there are 2 partitions of 17 into seven primes: [2,2,2,2,2,2,5] and [2,2,2,2,3,3,3].

Crossrefs

Column k=7 of A117278.

Number of partitions of n into r primes for r = 1-10: A010051, A061358, A068307, A259194, A259195, A259196, this sequence, A259198, A259200, A259201.

Cf. A000040.

Sequence in context: A070172 A273353 A367410 * A309559 A130128 A210556

Adjacent sequences: A259194 A259195 A259196 * A259198 A259199 A259200

Keyword

nonn,easy

Author

Doug Bell, Jun 20 2015

Status

approved