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).

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

Author

Karl-Heinz Hofmann, Jul 16 2022

Keywords

• nonn

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.

Examples

			See the PDF in links.
		

Links

• Karl-Heinz Hofmann, Examples of a(1..8)
• Wikipedia, Archimedean spiral

Crossrefs

Cf. A000328, A295344, A046109.