A344254 Number of partitions of n into 7 semiprime parts.

1, 0, 1, 0, 1, 1, 2, 1, 2, 1, 4, 3, 5, 3, 5, 5, 7, 8, 9, 7, 11, 12, 16, 15, 16, 16, 21, 23, 26, 27, 31, 31, 38, 41, 45, 46, 50, 55, 62, 66, 71, 77, 85, 85, 97, 105, 113, 117, 124, 136, 149, 156, 167, 179, 189, 199, 214, 235

Offset

28,7

Links

Alois P. Heinz, Table of n, a(n) for n = 28..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)} [Omega(o) = Omega(m) = Omega(l) = Omega(k) = Omega(j) = Omega(i) = Omega(n-i-j-k-l-m-o) = 2], where Omega is the number of prime factors with multiplicity (A001222) and [ ] is the (generalized) Iverson bracket.

a(n) = [x^n y^7] 1/Product_{j>=1} (1-y*x^A001358(j)). - Alois P. Heinz, May 21 2021

Crossrefs

Cf. A001222 (Omega), A001358.

Column k=7 of A344447.

Sequence in context: A308213 A226279 A344246 * A344255 A344256 A344257

Adjacent sequences: A344251 A344252 A344253 * A344255 A344256 A344257

Keyword

nonn

Author

Wesley Ivan Hurt, May 12 2021

Status

approved