A240600 Number of partially filled hexagons in the first 120-degree circular sector of hexagonal lattice A_2 centered at deep hole along the edge of a circle also centered at the deep hole.

0, 1, 1, 2, 2, 4, 3, 3, 3, 5, 4, 5, 5, 7, 5, 5, 5, 6, 6, 8, 6, 8, 7, 7, 7, 9, 7, 7, 7, 9, 8, 9, 9, 11, 9, 11, 9, 9, 9, 11, 9, 10, 10, 12, 10, 12, 12, 14, 12, 14, 13, 13, 11, 11, 11, 13, 13, 15, 13, 13, 13, 15, 14

Offset: 0

Author

Rajan Murthy, Apr 09 2014

Keywords

• nonn

Comments

A(n) alternates between the numbers for circles which intersect points on the A2 lattice and the numbers for circles which pass in between the points on a lattice.

Examples

			for n = 1, the squared radius is in the open interval (0,1) and the corresponding circle passes through 1 hexagon.
for n = 14, the squared radius is 13 with the corresponding circle passing through the furthest corner of 2 hexagons and passing through 5 hexagons.
		

Links

• Rajan Murthy, Code for computing 3*A(n) as a function of R^2 (scilab)

Crossrefs

A038588 gives the number of hexagons completely encircled in all three circular sectors.

Squared radii of alternate entries is given by the Loeschian numbers A003136.

A234300 is the analog for the 2-d Cartesian lattice.

A237708 is the analog for the 3-d Cartesian lattice.

A239353 is the analog for the 4-d Cartesian lattice.