A177369 Expansion of g.f.: (1+4*x-4*x^2)/(1-3*x-4*x^2+4*x^3).

1, 7, 21, 87, 317, 1215, 4565, 17287, 65261, 246671, 931909, 3521367, 13305053, 50272991, 189953717, 717732903, 2711921613, 10246881583, 38717399589, 146292038647

Offset

1,2

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

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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 (3,4,-4).

Formula

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

a(1)=1, a(2)=7, a(3)=21, a(n)=3*a(n-1)+4*a(n-2)-4*a(n-3). - Harvey P. Dale, May 10 2015

Mathematica

CoefficientList[Series[(1+4x-4x^2)/(1-3x-4x^2+4x^3), {x, 0, 20}], x] (* or *) LinearRecurrence[{3, 4, -4}, {1, 7, 21}, 20] (* Harvey P. Dale, May 10 2015 *)

Prog

(PARI) a(n)=([0, 1, 0; 0, 0, 1; -4, 4, 3]^(n-1)*[1; 7; 21])[1, 1] \\ Charles R Greathouse IV, May 30 2026

Crossrefs

Sequence in context: A110683 A092785 A114902 * A164544 A100025 A121157

Adjacent sequences: A177366 A177367 A177368 * A177370 A177371 A177372

Keyword

nonn,easy

Author

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

Extensions

Definition clarified by Harvey P. Dale, May 10 2015

Status

approved