A337790 - OEIS

A337790

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

3, 57, 306, 837, 1335, 2073, 3033, 4395, 6147, 8469, 11253, 14907, 19263, 24819, 31197, 38823, 47619

(list; graph; refs; listen; history; text; internal format)

OFFSET

0,1

COMMENTS

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

LINKS

Table of n, a(n) for n=0..16.

Scott R. Shannon, Image for the figure showing the vertex counts for n=1.

Scott R. Shannon, Image for the figure showing the vertex counts for n=2.

Scott R. Shannon, Image for the figure showing the vertex counts for n=3.

Scott R. Shannon, Image for the figure showing the vertex counts for n=4.

Scott R. Shannon, Image for the figure showing the vertex counts for n=5.

Scott R. Shannon, Image for the figure showing the vertex counts for n=6.

EXAMPLE

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

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.

CROSSREFS

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

Sequence in context: A122548 A078728 A032696 * A131466 A171356 A060483

Adjacent sequences: A337787 A337788 A337789 * A337791 A337792 A337793

KEYWORD

nonn,more

AUTHOR

Scott R. Shannon and N. J. A. Sloane, Sep 22 2020

STATUS

approved