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

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`%I #9 Jan 03 2015 08:37:58
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`%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,
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`%T 82,83,85,89,93,95,99,103,107,115,117,119,121,129,133,135,137,141,143,
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`%U 147,149,150,154,158,160,161,169,173,177,179,183,185,187,191,193,195,199,203,205,207,211,213
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`%N Circular disk sequence for the lattice of the Archimedean tiling (4,8,8).
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`%C For the squares of the radii of the lattice point hitting circles of the Archimedean tiling (4,8,8) see A251629 and A251631.
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`%C The first differences for this sequence are given in A251633.
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`%C See the link for more details.
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`%H Wolfdieter Lang, <a href="/A251632/a251632_1.pdf">On lattice point circles for the Archimedean tiling (4,8,8).</a>
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`%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Tiling_by_regular_polygons#Archimedean.2C_uniform_or_semiregular_tilings">Archimedean tilings</a>
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`%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.
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`%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.
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`%Y Cf. A251629, A251631, A251633.
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`%K nonn,easy
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`%O 0,2
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`%A _Wolfdieter Lang_, Jan 02 2015
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