A390082 The number of irreducible zero-sum subsets of {-n..n} that contain -n but not n.

0, 0, 1, 2, 4, 10, 16, 33, 58, 107, 177, 309, 512, 855, 1396, 2213, 3464, 5443, 8311, 12684, 19149, 28407, 41965, 61222, 88912, 126832, 181455, 254583, 358776, 497709, 691913, 945065, 1300943, 1755378, 2391556, 3181281, 4291083

Offset

1,4

Comments

A zero-sum subsets of {-n..n} is called irreducible if it doesn't contain any smaller zero-sum subset.

Links

Table of n, a(n) for n=1..37.

Chinese BBS, Balanced samples of the initial segment of natural numbers (in Chinese).

Formula

a(n) = (A389802(2*n+1) - A389802(2*n-1) - 1)/2.

a(n) = (A389803(n) - A389803(n-1) - 1)/2.

Example

For n = 3, a(3) = 1, since {-3..3} has only one such subsets: {1,2,-3}.
For n = 4, a(4) = 2, since {-4..4} has two such subsets: {1, 3, -4}, {-1, 2, 3, -4}.
For n = 5, a(5) = 4, since {-5..5} has 4 such subsets: {1, 4, -5}, {2, 3, -5}, {-1, 2, 4, -5}, {-2, 3, 4, -5}.

Crossrefs

Cf. A389802, A389803, A389806, A390083.

Sequence in context: A228136 A393815 A153927 * A117862 A105024 A050871

Adjacent sequences: A390079 A390080 A390081 * A390083 A390084 A390085

Keyword

nonn

Author

Hu Junhua, Oct 28 2025

Status

approved