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

Table of n, a(n) for n=1..26.

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

Index entries for linear recurrences with constant coefficients, signature (2,8,4).

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

Adjacent sequences:  A287482 A287483 A287484 * A287486 A287487 A287488

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 | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified January 29 00:42 EST 2022. Contains 350670 sequences. (Running on oeis4.)