A177371 Expansion of (1+12*x-24*x^2+8*x^4)/((1-8*x+4*x^2+4*x^3)*(1+2*x-2*x^2)).

1, 18, 98, 812, 5748, 43120, 316600, 2343120, 17290256, 127726400, 943159584, 6965532736, 51439836352, 379886330112, 2805462584192, 20718413985536, 153005867110656, 1129951564794880, 8344715027364352, 61625891492889600

Offset

0,2

References

S. Kitaev, A. Burstein and T. Mansour. Counting independent sets in certain classes of (almost) regular graphs, Pure Mathematics and Applications (PU.M.A.) 19 (2008), no. 2-3, 17-26.

Links

Table of n, a(n) for n=0..19.

S. Kitaev, A. Burstein and T. Mansour. Counting independent sets in certain classes of (almost) regular graphs

Index entries for linear recurrences with constant coefficients, signature (6, 14, -28, 0, 8).

Formula

From Harvey P. Dale, May 09 2011: (Start)

G.f.: (1+12*x-24*x^2+8*x^4)/((1-8*x+4*x^2+4*x^3)*(1+2*x-2*x^2)).

a(0)=1, a(1)=18, a(2)=98, a(3)=812, a(4)=5748, a(n)=6a(n-1)+ 14a(n-2) -28a(n-3) +8a(n-5). (End)

Mathematica

CoefficientList[Series[(1+12x-24x^2+8x^4)/((1-8x+4x^2+4x^3)(1+2x-2x^2)), {x, 0, 20}], x] (* or *) LinearRecurrence[{6, 14, -28, 0, 8}, {1, 18, 98, 812, 5748}, 20]  (* Harvey P. Dale, May 09 2011 *)

Crossrefs

Sequence in context: A118864 A118606 A318063 * A044269 A044650 A008920

Adjacent sequences: A177368 A177369 A177370 * A177372 A177373 A177374

Keyword

nonn

Author

Signy Olafsdottir (signy06(AT)ru.is), May 07 2010

Extensions

Definition clarified by Harvey P. Dale, May 09 2011

Status

approved