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A251627
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Circular disk sequence for the lattice of the Archimedean tiling (3,4,6,4).
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4
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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
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0,2
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COMMENTS
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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.
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LINKS
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Table of n, a(n) for n=0..54.
Wolfdieter Lang, On lattice point circles for the Archimedean tiling (3,4,6,4)
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FORMULA
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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.
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EXAMPLE
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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.
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CROSSREFS
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Cf. A249870, A249871, A251628.
Sequence in context: A116024 A115913 A200268 * A128161 A141106 A047478
Adjacent sequences: A251624 A251625 A251626 * A251628 A251629 A251630
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KEYWORD
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nonn,easy
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AUTHOR
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Wolfdieter Lang, Dec 09 2014
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STATUS
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approved
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