The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A344907 Number of polygon edges formed when every pair of vertices of a regular (2n-1)-gon are joined by an infinite line. 4
0, 3, 30, 189, 684, 1815, 3978, 7665, 13464, 22059, 34230, 50853, 72900, 101439, 137634, 182745, 238128, 305235, 385614, 480909, 592860, 723303, 874170, 1047489, 1245384, 1470075, 1723878, 2009205, 2328564, 2684559, 3079890, 3517353, 3999840, 4530339, 5111934, 5747805, 6441228, 7195575 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
COMMENTS
This sequences gives the number of polygon edges formed when connecting every pair of vertices of a regular polygon, with an odd number of vertices, by an infinite line.
A bisection of A344899. - N. J. A. Sloane, Sep 12 2021
See A344857 for other examples and images of the polygons.
LINKS
FORMULA
a(n) = 4*n^4 - 22*n^3 + 44*n^2 - 35*n + 9 (see Sidorenko link in A344857 for proof).
From Stefano Spezia, Jun 10 2021: (Start)
G.f.: 3*x^2*(1 + 5*x + 23*x^2 + 3*x^3)/(1 - x)^5.
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5) for n > 5. (End)
EXAMPLE
a(3) = 30 as the five connected vertices form a pentagon with fives lines along the pentagon's edges, fifteen lines inside forming eleven polygons, and ten lines outside forming another five triangles. In all these sixteen polygons form thirty edges. Twenty infinite edges between the outer unbounded regions are also formed.
PROG
(Python)
def A344907(n): return n*(n*(n*(4*n - 22) + 44) - 35) + 9 # Chai Wah Wu, Sep 12 2021
CROSSREFS
Cf. A344899 (number of edges for all n-gons), A344866 (number of polygon), A146212, A344857, A344311, A007678, A331450, A344938.
See also A347322.
Sequence in context: A013220 A177727 A132413 * A032263 A003771 A121100
KEYWORD
nonn,easy
AUTHOR
Scott R. Shannon, Jun 02 2021
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 16 02:19 EDT 2024. Contains 373416 sequences. (Running on oeis4.)