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A348235 List of distinct squared distances from all points of Don Wilkinson's 123-circle packing to a fixed type (c) point. 2
0, 16, 25, 36, 52, 64, 97, 100, 144, 153, 160, 180, 208, 225, 241, 256, 288, 292, 324, 340, 369, 388, 400, 409, 436, 457, 468, 481, 544, 576, 580, 585, 592, 612, 625, 640, 720, 724, 745, 784, 793, 820, 832, 841, 865, 873, 900, 916, 928, 964, 976 (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 (c) point.
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.
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.
CROSSREFS
Sequence in context: A030666 A030676 A264604 * A218439 A192689 A002644
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 08 2021
STATUS
approved

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Last modified May 21 22:16 EDT 2024. Contains 372741 sequences. (Running on oeis4.)