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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).

%I A355760 #40 Aug 07 2022 07:53:45
%S A355760 1,2,8,21,40,64,97,132,178,228,282,350,415,492,574,660,756,855,962,
%T A355760 1076,1195,1322,1451,1590,1736,1885,2044,2204,2378,2552,2734,2922,
%U A355760 3116,3317,3525,3741,3960,4187,4416,4655,4900,5154,5410,5674,5946,6223,6502,6791,7087,7391,7698
%N 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).
%C A355760 Grid points coincident with the outer boundary of the spiral are included.
%C A355760 The spiral figure is closed with a line from (n, 0) to (n-1, 0).
%C A355760 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.
%H A355760 Karl-Heinz Hofmann, <a href="/A355760/a355760.pdf">Examples of a(1..8)</a>
%H A355760 Wikipedia, <a href="https://en.wikipedia.org/wiki/Archimedean_spiral">Archimedean spiral</a>
%e A355760 See the PDF in links.
%Y A355760 Cf. A000328, A295344, A046109.
%K A355760 nonn
%O A355760 0,2
%A A355760 _Karl-Heinz Hofmann_, Jul 16 2022