

A251627


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


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
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OFFSET

0,2


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.


LINKS



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.


EXAMPLE

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.


CROSSREFS



KEYWORD

nonn,easy


AUTHOR



STATUS

approved



