A292276 a(n) = number of vertices of the convex hull of the set of points of norm <= n^2 in square lattice.

1, 4, 4, 8, 12, 12, 12, 12, 20, 12, 20, 20, 20, 20, 20, 20, 20, 24, 28, 20, 20, 20, 36, 36, 28, 20, 36, 36, 36, 36, 28, 36, 36, 36, 44, 36, 36, 36, 36, 52, 44, 36, 36, 36, 52, 44, 52, 52, 44, 52, 44, 60, 52, 44, 52, 44, 52, 52, 52, 52, 60, 52, 52, 52, 68, 44

Offset

0,2

Comments

The convex hull of a finite point set in dimension 2, say S, forms a convex polygon whose vertices are in S.

For any n >= 0, A000328(n) gives the number of elements of the set of points of norm <= n^2 in square lattice.

For symmetry reasons, a(n) is a multiple of 4 for any n > 0.

Links

Table of n, a(n) for n=0..65.

Rémy Sigrist, C++ program for A292276

Rémy Sigrist, Illustration of the convex hulls for n=0..10

Wikipedia, Convex hull of a finite point set

Example

See Links section.

Prog

(C++) See Links section.

Crossrefs

Cf. A000328, A046109.

Sequence in context: A301705 A309456 A004024 * A278083 A086663 A003829

Adjacent sequences: A292273 A292274 A292275 * A292277 A292278 A292279

Keyword

nonn

Author

Rémy Sigrist, Sep 13 2017

Status

approved