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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Oct 08 2021
STATUS
approved