A293596 - OEIS

%I #15 Oct 15 2017 01:21:37

%S 1,2,2,3,4,4,3,4,6,6,5,4,6,6,8,7,6,6,6,8,9,10,10,8,8,7,8,10,10,12,13,

%T 12,12,10,10,9,10,12,12,14,13,14,14,14,12,12,9,10,14,14,16,16,17,16,

%U 18,16,16,14,13,10,14,14,14,18,18,19,18,20,18,16,18

%N The number of vertices on successive convex layers of the positive quadrant of the two-dimensional integer grid.

%H David Eppstein, Sariel Har-Peled, and Gabriel Nivasch, <a href="https://arxiv.org/abs/1710.03960">Grid peeling and the affine curve-shortening flow</a>, arXiv:1710.03960 [cs.CG], 2017, Fig. 5. To appear in ALENEX 2018.

%e a(1) is 1 because the first convex layer only has one vertex, (0,0).

%e a(2) is 2 because the second convex layer has the two vertices (0,1) and (1,0).

%e The illustration for a(5)=4, a(10)=6, ..., a(30)=12 see in Fig. 3 of the Eppstein, Har-Peled & Nivasch reference.

%Y Cf. A290966.

%K nonn

%O 1,2

%A _David Eppstein_, Oct 12 2017