login
The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A301772 Number of odd chordless cycles in the n-antiprism graph. 0
0, 2, 0, 2, 8, 2, 24, 16, 48, 92, 100, 310, 344, 808, 1344, 2102, 4480, 6462, 13092, 21662, 37488, 69904, 113652, 212844, 359856, 636402, 1134068, 1937072, 3493120, 6012746, 10639264, 18706394, 32550976, 57727738, 100407848, 177116816, 310493720, 543717148 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Sequence extended to a(0)-a(3) using the formula/recurrence (actual 3-antiprism count is 0).

LINKS

Table of n, a(n) for n=0..37.

Eric Weisstein's World of Mathematics, Antiprism Graph

Eric Weisstein's World of Mathematics, Chordless Cycle

Index entries for linear recurrences with constant coefficients, signature (0, 2, 2, -1, 2, -1).

FORMULA

a(n) = 2*a(n-2) + 2*a(n-3) - a(n-4) + 2*a(n-5) - a(n-6).

G.f.: 2*x*(1 - x^2 + 2*x^3)/(1 - 2*x^2 - 2*x^3 + x^4 - 2*x^5 + x^6).

MATHEMATICA

Table[(RootSum[-1 + #1 - 2 #1^2 + #1^3 &, #1^n &] - RootSum[-1 + #1 + 2 #1^2 + #1^3 &, #1^n &])/2, {n, 0, 20}]

LinearRecurrence[{0, 2, 2, -1, 2, -1}, {0, 2, 0, 2, 8, 2}, 20]

CoefficientList[Series[2 x (1 - x^2 + 2 x^3)/(1 - 2 x^2 - 2 x^3 + x^4 - 2 x^5 + x^6), {x, 0, 20}], x]

CROSSREFS

Sequence in context: A211888 A293783 A274541 * A021497 A201735 A029593

Adjacent sequences:  A301769 A301770 A301771 * A301773 A301774 A301775

KEYWORD

nonn

AUTHOR

Eric W. Weisstein, Mar 26 2018

STATUS

approved

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

License Agreements, Terms of Use, Privacy Policy. .

Last modified September 18 06:42 EDT 2021. Contains 347510 sequences. (Running on oeis4.)