A023024 Number of partitions of n into 4 unordered relatively prime parts.

1, 1, 2, 3, 4, 6, 8, 11, 12, 18, 20, 26, 29, 39, 39, 54, 54, 69, 73, 94, 89, 119, 118, 144, 145, 185, 169, 225, 215, 259, 258, 317, 291, 378, 357, 423, 410, 511, 457, 588, 547, 639, 626, 764, 679, 861, 792, 933, 896, 1089, 963, 1203, 1112, 1296, 1240, 1495, 1302, 1650

Offset

4,3

Links

Table of n, a(n) for n=4..61.

Index entries for sequences related to partitions

Formula

G.f.: Sum_{k>=1} mu(k)*x^(4*k) / Product_{j=1..4} (1 - x^(j*k)). - Ilya Gutkovskiy, Aug 31 2019

a(n) = Sum_{k=1..floor(n/4)} Sum_{j=k..floor((n-k)/3)} Sum_{i=j..floor((n-j-k)/2)} [gcd(k,j,i,n-i-j-k) = 1], where [ ] is the Iverson bracket. - Wesley Ivan Hurt, Jan 17 2021

Mathematica

Table[Sum[Sum[Sum[KroneckerDelta[GCD[k, j, i, (n - i - j - k)], 1], {i, j,  Floor[(n - j - k)/2]}], {j, k, Floor[(n - k)/3]}], {k, Floor[n/4]}], {n, 4, 80}] (* Wesley Ivan Hurt, Jan 17 2021 *)

Crossrefs

Column 4 of A282750.

Sequence in context: A353721 A263132 A018502 * A018362 A033056 A060469

Adjacent sequences: A023021 A023022 A023023 * A023025 A023026 A023027

Keyword

nonn

Author

David W. Wilson

Status

approved