A293596 The number of vertices on successive convex layers of the positive quadrant of the two-dimensional integer grid.
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, 12, 12, 10, 10, 9, 10, 12, 12, 14, 13, 14, 14, 14, 12, 12, 9, 10, 14, 14, 16, 16, 17, 16, 18, 16, 16, 14, 13, 10, 14, 14, 14, 18, 18, 19, 18, 20, 18, 16, 18
Offset: 1
Keywords
Examples
a(1) is 1 because the first convex layer only has one vertex, (0,0). a(2) is 2 because the second convex layer has the two vertices (0,1) and (1,0). The illustration for a(5)=4, a(10)=6, ..., a(30)=12 see in Fig. 3 of the Eppstein, Har-Peled & Nivasch reference.
Links
- David Eppstein, Sariel Har-Peled, and Gabriel Nivasch, Grid peeling and the affine curve-shortening flow, arXiv:1710.03960 [cs.CG], 2017, Fig. 5. To appear in ALENEX 2018.
Crossrefs
Cf. A290966.