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Gilberto Brito de Almeida has authored 2 sequences.

A374773 a(n):= #G_{2n}(3n+1) for n >= 1, where G_{2n}(3n+1) is the set of all pure (2n)-sparse gapset of genus 3n+1 and n a positive integer.

Original entry on oeis.org

3, 8, 22, 54, 135, 331, 808

Offset: 1

Gilberto Brito de Almeida, Jul 19 2024

Gilberto B. Almeida Filho and Matheus Bernardini On pure kappa-sparse gapsets, Semigroup Forum, Vol. 104 (2022), pp. 213-227.
Gilberto Brito and Stéfani Vieira, A certain sequence on pure kappa-sparse gapsets, arXiv:2407.21563 [math.CO], 2024. See pp. 1-2.

Cf. A348619.

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

Original entry on oeis.org

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

Offset: 0

Gilberto Brito de Almeida, Oct 25 2021

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.

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.

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User: Gilberto Brito de Almeida

A374773 a(n):= #G_{2n}(3n+1) for n >= 1, where G_{2n}(3n+1) is the set of all pure (2n)-sparse gapset of genus 3n+1 and n a positive integer.

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

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