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!)
A287485 Number of independent vertex sets and vertex covers in the n-web graph. 0
2, 20, 68, 304, 1232, 5168, 21408, 89088, 370112, 1538560, 6394368, 26577664, 110464512, 459127808, 1908282368, 7931445248, 32965660672, 137016012800, 569483091968, 2366956929024, 9837842644992, 40889273090048, 169949115056128, 706363785412608, 2935877583634432, 12202461910794240 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
LINKS
Eric Weisstein's World of Mathematics, Independent Vertex Set
Eric Weisstein's World of Mathematics, Vertex Cover
Eric Weisstein's World of Mathematics, Web Graph
FORMULA
G.f.: -2*x*(1 + 8*x + 6*x^2)/(-1 + 2*x + 8*x^2 + 4*x^3).
a(n) = 2*a(n-1) + 8*a(n-2) + 4*a(n-3).
MATHEMATICA
Table[RootSum[-4 - 8 # - 2 #^2 + #^3 &, #^n &], {n, 20}]
LinearRecurrence[{2, 8, 4}, {2, 20, 68}, 20]
CoefficientList[Series[-2 (1 + 8 x + 6 x^2)/(-1 + 2 x + 8 x^2 + 4 x^3), {x, 0, 20}], x] (* Eric W. Weisstein, Sep 27 2017 *)
PROG
(PARI) Vec(-2*x*(1+8*x+6*x^2)/(-1+2*x+8*x^2+4*x^3) + O(x^30)) \\ Michel Marcus, Sep 27 2017
CROSSREFS
Sequence in context: A183907 A216609 A226394 * A003283 A259110 A135188
KEYWORD
nonn,easy
AUTHOR
Eric W. Weisstein, May 25 2017
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 March 29 00:26 EDT 2024. Contains 371264 sequences. (Running on oeis4.)