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A028860 a(n+2) = 2*a(n+1) + 2*a(n). 10
-1, 1, 0, 2, 4, 12, 32, 88, 240, 656, 1792, 4896, 13376, 36544, 99840, 272768, 745216, 2035968, 5562368, 15196672, 41518080, 113429504, 309895168, 846649344, 2313089024, 6319476736, 17265131520 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

COMMENTS

a(n+1) is the top left entry of the n-th power of the 3X3 matrix [0, 1, 1; 1, 1, 1; 1, 1, 1]. - R. J. Mathar, Feb 04 2014

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Martin Burtscher, Igor Szczyrba, RafaƂ Szczyrba, Analytic Representations of the n-anacci Constants and Generalizations Thereof, Journal of Integer Sequences, Vol. 18 (2015), Article 15.4.5.

INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 924

Tanya Khovanova, Recursive Sequences

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

FORMULA

a(n) = 4*A028859(n-4), for n>3.

G.f.: -(1-3*x)/(1-2*x-2*x^2). a(n) = 3*A002605(n-1) -A002605(n). [From R. J. Mathar, Nov 27 2008]

If p[i]=fibonacci(2i-4) and if A is the Hessenberg matrix of order n defined by: A[i,j]=p[j-i+1], (i<=j), A[i,j]=-1, (i=j+1), and A[i,j]=0 otherwise. Then, for n>=1, a(n-1)= det A. [From Milan Janjic, May 08 2010]

a(n) = (2*sqrt(3)-3)/6*(1+sqrt(3))^n - (2*sqrt(3)+3)/6*(1-sqrt(3))^n. - Sergei N. Gladkovskii, Jul 18 2012

MATHEMATICA

(With a different offset) M = {{0, 2}, {1, 2}} v[1] = {0, 1} v[n_] := v[n] = M.v[n - 1] a = Table[Abs[v[n][[1]]], {n, 1, 50}] - Roger L. Bagula, May 29 2005

LinearRecurrence[{2, 2}, {-1, 1}, 40] (* Harvey P. Dale, Dec 13 2012 *)

PROG

(Haskell)

a028860 n = a028860_list !! n

a028860_list =

   -1 : 1 : map (* 2) (zipWith (+) a028860_list (tail a028860_list))

-- Reinhard Zumkeller, Oct 15 2011

CROSSREFS

Cf. A026150, A030195, A080040, A083337, A106435, A108898, A125145.

Sequence in context: A242659 A109388 A181329 * A152035 A026151 A025178

Adjacent sequences:  A028857 A028858 A028859 * A028861 A028862 A028863

KEYWORD

sign

AUTHOR

N. J. A. Sloane. Edited by N. J. A. Sloane, Apr 11 2009

STATUS

approved

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Last modified March 28 07:54 EDT 2017. Contains 284182 sequences.