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List of distinct squared distances from all points of Don Wilkinson's 123-circle packing to a fixed type (c) point.
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%I #16 Dec 16 2021 20:12:00

%S 0,16,25,36,52,64,97,100,144,153,160,180,208,225,241,256,288,292,324,

%T 340,369,388,400,409,436,457,468,481,544,576,580,585,592,612,625,640,

%U 720,724,745,784,793,820,832,841,865,873,900,916,928,964,976

%N List of distinct squared distances from all points of Don Wilkinson's 123-circle packing to a fixed type (c) point.

%C Wilkinson's 123-circle packing (that is my name for it) is a packing of non-overlapping circles in the plane, and can be seen in the links in A348227. There are three sizes of circles: (a) radius 1, (b) radius 2, and (c) radius 3. See A348227 for further information.

%C A convenient set of coordinates for the centers are: (a) radius 1: the points (8*i, 6*j), (b) radius 2: the points (8*i, 6*j+3), and (c) radius 3: the points (8*i+4, 6*j), where i and j take all integer values.

%C The present sequence lists the exponents in the theta series with respect to a type (c) point.

%C This theta series begins 1 + 2*q^16 + 4*q^25 + 2*q^36 + 4*q^52 + 2*q^64 + 4*q^97 + 4*q^100 + 4*q^144 + 4*q^153 + 4*q^160 + 4*q^180 + ... but the terms are too sparse for an OEIS entry.

%H N. J. A. Sloane, <a href="/A348227/a348227_3.pdf">Graph formed by centers of Wilkinson's 123-circle packing</a> (type (a), black: center of circle of radius 1; type (b), green: center of circle of radius 2; type (c), red: center of circle of radius radius 3). This figure should be rotated counterclockwise by 90 degrees in order to match the other figures in A348227.

%Y Cf. A348227-A348239.

%K nonn

%O 1,2

%A _N. J. A. Sloane_, Oct 08 2021