A337700 Place two n-gons with radii 1 and 2 concentrically, forming an annular area between them. Connect all the vertices with line segments that lie entirely within that area. Then a(n) is the number of regions in that figure.

12, 16, 20, 24, 63, 72, 315, 350, 385, 408, 767, 826, 2085, 2224, 2363, 2340, 3762, 3960, 7644, 8008, 8372, 8448, 11850, 12324, 20466, 21224, 21982, 21480, 28985, 29920, 45177, 46546, 47915, 48456, 60273, 61902, 87555, 89800, 92045, 91896, 111972, 114576

Offset

3,1

Comments

Because of symmetry, a(n) is divisible by n.

Links

Lars Blomberg, Table of n, a(n) for n = 3..102

Lars Blomberg, Illustration for n = 3

Lars Blomberg, Illustration for n = 4

Lars Blomberg, Illustration for n = 5

Lars Blomberg, Illustration for n = 7

Lars Blomberg, Illustration for n = 10

Lars Blomberg, Illustration for n = 29

Lars Blomberg, Illustration for n = 32

Formula

a(n) = A337702(n) - A337701(n) by Euler's formula, there being 1 hole.

Crossrefs

Cf. A337701, A337702, A337703.

Sequence in context: A231903 A364405 A337703 * A243538 A183052 A344079

Adjacent sequences: A337697 A337698 A337699 * A337701 A337702 A337703

Keyword

nonn

Author

Lars Blomberg, Sep 16 2020

Status

approved