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Number of vertices in a Y-shaped polygon with equal arms of length n (see the Comments in A335861 for definition).
2

%I #10 Sep 26 2020 02:58:31

%S 3,57,306,837,1335,2073,3033,4395,6147,8469,11253,14907,19263,24819,

%T 31197,38823,47619

%N Number of vertices in a Y-shaped polygon with equal arms of length n (see the Comments in A335861 for definition).

%C See A335861 for a definition of the polygon and images for the number of regions.

%H Scott R. Shannon, <a href="/A337790/a337790.png">Image for the figure showing the vertex counts for n=1</a>.

%H Scott R. Shannon, <a href="/A337790/a337790_1.png">Image for the figure showing the vertex counts for n=2</a>.

%H Scott R. Shannon, <a href="/A337790/a337790_2.png">Image for the figure showing the vertex counts for n=3</a>.

%H Scott R. Shannon, <a href="/A337790/a337790_3.png">Image for the figure showing the vertex counts for n=4</a>.

%H Scott R. Shannon, <a href="/A337790/a337790_4.png">Image for the figure showing the vertex counts for n=5</a>.

%H Scott R. Shannon, <a href="/A337790/a337790_5.png">Image for the figure showing the vertex counts for n=6</a>.

%e a(0) = 3. A single triangle with no other polygons has three vertices.

%e a(1) = 57. With one square adjacent to each of the triangles sides the resulting line segments form 51 vertices shared by four polygons, 3 vertices shared by six polygons, and 3 vertices shared by seven polygons. This gives a total of 57 vertices. See the first linked image.

%Y Cf. A335861 (number of regions), A331456, A331452, A306302, A092867, A007678.

%K nonn,more

%O 0,1

%A _Scott R. Shannon_ and _N. J. A. Sloane_, Sep 22 2020