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A355760
a(n) is the number of grid points in a square lattice covered by the area enclosed by n loops of an Archimedean spiral with starting point (0, 0) and endpoint (n, 0).
2
1, 2, 8, 21, 40, 64, 97, 132, 178, 228, 282, 350, 415, 492, 574, 660, 756, 855, 962, 1076, 1195, 1322, 1451, 1590, 1736, 1885, 2044, 2204, 2378, 2552, 2734, 2922, 3116, 3317, 3525, 3741, 3960, 4187, 4416, 4655, 4900, 5154, 5410, 5674, 5946, 6223, 6502, 6791, 7087, 7391, 7698
OFFSET
0,2
COMMENTS
Grid points coincident with the outer boundary of the spiral are included.
The spiral figure is closed with a line from (n, 0) to (n-1, 0).
Conjecture: Only lattice points on the positive x-axis are on the outer boundary of the spiral. It seems that the spiral passes all other grid points without hitting any.
EXAMPLE
See the PDF in links.
CROSSREFS
KEYWORD
nonn
AUTHOR
Karl-Heinz Hofmann, Jul 16 2022
STATUS
approved