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

1,2

Links

Table of n, a(n) for n=1..71.

David Eppstein, Sariel Har-Peled, and Gabriel Nivasch, Grid peeling and the affine curve-shortening flow, arXiv:1710.03960 [cs.CG], 2017-2018, Fig. 9. Published in Proceedings of the Twentieth Workshop on Algorithm Engineering and Experiments (ALENEX 2018), pp. 109-116, SIAM. See also the version in Experimental Mathematics, 29 (2020), 306-316.

Example

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. 6 of the Eppstein, Har-Peled & Nivasch reference.

Crossrefs

Cf. A290966, A392196 (3-dimensional analog).

Sequence in context: A326846 A243220 A334593 * A301977 A085430 A379719

Adjacent sequences: A293593 A293594 A293595 * A293597 A293598 A293599

Keyword

nonn

Author

David Eppstein, Oct 12 2017

Status

approved