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A348233 List of distinct squared distances from all points of Don Wilkinson's 123-circle 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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
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.
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 123-circle 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 next-closest are the two type (c) points at distance 4, so a(3) = 4^2 = 16.
And so on.
CROSSREFS
Sequence in context: A153362 A039788 A175652 * A110833 A225808 A076621
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 08 2021
STATUS
approved

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Last modified April 13 12:28 EDT 2024. Contains 371641 sequences. (Running on oeis4.)