A251627 Circular disk sequence for the lattice of the Archimedean tiling (3,4,6,4).

1, 5, 7, 9, 13, 14, 18, 25, 29, 33, 35, 39, 43, 45, 49, 51, 55, 57, 59, 63, 69, 73, 77, 79, 83, 89, 93, 97, 99, 101, 103, 107, 109, 113, 117, 121, 123, 127, 129, 133, 134, 136, 140, 144, 146, 158, 160, 164, 165, 169, 173, 177, 181, 183, 187

Offset: 0

Author

Wolfdieter Lang, Dec 09 2014

Keywords

• nonn
• easy

Comments

For the squares of the radii of the lattice point hitting circles of the Archimedean tiling (3,4,6,4) see A249870 and A249871.

The first differences for this sequence are given in A251628.

Examples

			n=4: The radius of the disk is R(4) = sqrt(2 + sqrt(3)), approximately 1.932. The lattice points for this R(n)-disk are the origin, four points on the circle with radius R(1) = 1, two points on the circle with radius R(2) = sqrt(2), two points on the circle with radius R(3) = sqrt(3) and 4 points on the circle with radius R(4) = sqrt(2+sqrt(3)), all together 1 + 4 + 2 + 2 + 4 = 13 = a(4) lattice points. See Figure 3 of the note given in the link.
		

Links

• Wolfdieter Lang, On lattice point circles for the Archimedean tiling (3,4,6,4)

Crossrefs

Cf. A249870, A249871, A251628.

Formula

a(n) is the number of lattice points of the Archimedean tiling (3,4,6,4) on the boundary and the interior of the circular disk belonging to the radius R(n) = sqrt(A249870(n) + A249871(n)* sqrt(3)), for n >= 0.