A348619 a(n) = #G_{2n}(3n) for n >= 0, where G_{K}(N) is the set of pure K-sparse gapset of genus N.

1, 2, 5, 12, 30, 70, 167, 395, 936, 2212

Offset: 0

Author

Gilberto Brito de Almeida, Oct 25 2021

Keywords

• nonn
• hard
• more

Comments

A 'gapset' is a finite subset G of IN, ordered in the natural order, satisfying the postulate: 'If z in G and z = x + y for some x, y in IN, then x or y is in G.' G is a 'gapset of genus n' means that G has n elements. G is a 'k-sparse gapset' if the distance between any consecutive elements of G is at most k. A 'pure k-sparse gapset' G is a k-sparse gapset such there exist consecutive elements l and l' in G which assume this upper bound, i.e., such that l' - l = k.

Links

• Matheus Bernardini and Gilberto Brito, On Pure k-sparse gapsets, arXiv:2106.13296 [math.CO], 2021.
• Gilberto Brito and Stéfani Vieira, A certain sequence on pure kappa-sparse gapsets, arXiv:2407.21563 [math.CO], 2024. See p. 2.