A348619 - OEIS

%I #40 Aug 06 2024 21:54:12

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

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

%C 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.

%H Matheus Bernardini and Gilberto Brito, <a href="https://arxiv.org/abs/2106.13296">On Pure k-sparse gapsets</a>, arXiv:2106.13296 [math.CO], 2021.

%H Gilberto Brito and Stéfani Vieira, <a href="https://arxiv.org/abs/2407.21563">A certain sequence on pure kappa-sparse gapsets</a>, arXiv:2407.21563 [math.CO], 2024. See p. 2.

%K nonn,hard,more

%O 0,2

%A _Gilberto Brito de Almeida_, Oct 25 2021