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Number of vertices of a hexagonal tessellation that lie on subsequent circles centered at a vertex of one hexagon.
2

%I #56 Jun 21 2022 14:58:50

%S 1,3,6,3,6,6,6,6,3,6,12,3,6,6,6,6,6,12,6,6,9,6,12,6,12,3,6,6,6,6,6,6,

%T 12,12,12,6,3,6,6,6,12,6,12,3,6,6,12,12,6,6,18,6,6,12,6,6,9,12,6,6,6,

%U 12,12,6,6,9,6,12,6,6,12,12,6,6,12,6,12,6,6,6,12,12,3,12,6,6,24,6,12,6,3,12,6,6,12,6,6,12

%N Number of vertices of a hexagonal tessellation that lie on subsequent circles centered at a vertex of one hexagon.

%C Radii of these circles are square roots of A003136.

%C This is A113062 with zeros dropped. - _Andrey Zabolotskiy_, Jun 21 2022

%H Szymon Lukaszyk, <a href="https://www.researchgate.net/publication/345982332_A_short_note_about_the_geometry_of_graphene">A short note about the geometry of graphene</a>, ResearchGate, (2020).

%H Szymon Lukaszyk, <a href="/A338947/a338947.pdf">Illustration of the subsequent 51 radii around a hexagon vertex</a>.

%H S. Reich et al., <a href="https://www.ifkp.tu-berlin.de/fileadmin/i1/thomsen/publikationen/paper/290.pdf">Tight-binding description of graphene</a> (up to third-nearest neighbors circles).

%Y Cf. A003136, A113062; A338992 (similar but with circles centered at the center of one hexagon); A104888, A106030, A317990 (terms multiplied by 3 in agreement for up to 17 term).

%K nonn

%O 0,2

%A _Szymon Lukaszyk_, Nov 17 2020

%E a(0) changed from 0 to 1 by _Andrey Zabolotskiy_, Jun 21 2022