A251632 Circular disk sequence for the lattice of the Archimedean tiling (4,8,8).

1, 4, 5, 9, 15, 17, 19, 23, 28, 32, 33, 39, 41, 45, 47, 51, 53, 55, 59, 67, 71, 75, 78, 80, 82, 83, 85, 89, 93, 95, 99, 103, 107, 115, 117, 119, 121, 129, 133, 135, 137, 141, 143, 147, 149, 150, 154, 158, 160, 161, 169, 173, 177, 179, 183, 185, 187, 191, 193, 195, 199, 203, 205, 207, 211, 213

Offset: 0

Author

Wolfdieter Lang, Jan 02 2015

Keywords

• nonn
• easy

Comments

For the squares of the radii of the lattice point hitting circles of the Archimedean tiling (4,8,8) see A251629 and A251631.

The first differences for this sequence are given in A251633.

See the link for more details.

Examples

			n=4: The radius of the disk is R(4) = sqrt(3 + 2*sqrt(2)), approximately 2.4142. The lattice points for this R(4)-disk are the origin, three points on the circle with radius R(1) = 1, one point on the circle with radius R(2) = sqrt(2), four points on the circle with radius R(3) = sqrt(2 + sqrt(2)) and 6 points on the circle with radius R(4) = sqrt(3 + 2*sqrt(2)), all together 1 + 3 + 1 + 4 + 6 = 15 = a(4) lattice points.
		

Links

• Wolfdieter Lang, On lattice point circles for the Archimedean tiling (4,8,8).
• Wikipedia, Archimedean tilings

Crossrefs

Cf. A251629, A251631, A251633.

Formula

a(n) is the number of lattice points of the Archimedean tiling (4,8,8) on the boundary and the interior of the circular disk belonging to the radius R(n) = sqrt(A251629(n) + A251631(n)*sqrt(2)), for n >= 0.