A251632 - OEIS

%I #9 Jan 03 2015 08:37:58

%S 1,4,5,9,15,17,19,23,28,32,33,39,41,45,47,51,53,55,59,67,71,75,78,80,

%T 82,83,85,89,93,95,99,103,107,115,117,119,121,129,133,135,137,141,143,

%U 147,149,150,154,158,160,161,169,173,177,179,183,185,187,191,193,195,199,203,205,207,211,213

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

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

%C The first differences for this sequence are given in A251633.

%C See the link for more details.

%H Wolfdieter Lang, <a href="/A251632/a251632_1.pdf">On lattice point circles for the Archimedean tiling (4,8,8).</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tiling_by_regular_polygons#Archimedean.2C_uniform_or_semiregular_tilings">Archimedean tilings</a>

%F 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.

%e 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.

%Y Cf. A251629, A251631, A251633.

%K nonn,easy

%O 0,2

%A _Wolfdieter Lang_, Jan 02 2015