

A348233


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


0



0, 9, 16, 36, 52, 64, 73, 81, 100, 144, 145, 160, 180, 208, 225, 256, 265, 288, 289, 292, 324, 337, 340, 388, 400, 436, 441, 468, 481, 505, 544, 576, 580, 585, 592, 612, 640, 657, 697, 720, 724, 729, 784, 793, 801, 820, 832, 900, 916, 928, 964, 976, 985
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OFFSET

1,2


COMMENTS

Wilkinson's 123circle packing (that is my name for it) is a packing of nonoverlapping 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.
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.
The present sequence lists the exponents in the theta series with respect to a type (a) point.
This theta series begins 1 + 2*q^9 + 2*q^16 + 2*q^36 + 4*q^52 + 2*q^64 + 4*q^73 + 2*q^81 + 4*q^100 + 4*q^144 + 4*q^145 + 4*q^160 + 4*q^180 + ... but the terms are too sparse for an OEIS entry.


LINKS

N. J. A. Sloane, Graph formed by centers of Wilkinson's 123circle packing (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.


EXAMPLE

The point we start from is of course at distance 0 from itself, so a(1) = 0.
The closest points to a type (a) point are the two type (b) points at distance 3, so a(2) = 3^2 = 9.
The nextclosest are the two type (c) points at distance 4, so a(3) = 4^2 = 16.
And so on.


CROSSREFS



KEYWORD

nonn


AUTHOR



STATUS

approved



