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A106568 Expansion of 4*x/(1-4*x-4*x^2). 0
0, 4, 16, 80, 384, 1856, 8960, 43264, 208896, 1008640, 4870144, 23515136, 113541120, 548225024, 2647064576, 12781158400, 61712891904, 297976201216, 1438756372480, 6946930294784, 33542746669056, 161958707855360 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Previous name was: First entry of the vector (M^n)v, where M is the 2 X 2 matrix [[0,4],[1,4]] and v is the column vector [0,1].

LINKS

Table of n, a(n) for n=0..21.

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

Tanya Khovanova, Recursive Sequences

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

FORMULA

a(n) = 4 * A057087(n).

a(n) = A094013(n+1). [R. J. Mathar, Aug 24 2008]

a(0) = 0, a(1)=4, a(n)=4*a(n-1)+4*a(n-2) for n>2. G.f.: 4x/(1-4x-4x^2). [Philippe Deléham, Sep 19 2009]

G.f.: Q(0)- 1, where Q(k) = 1 + 2*(1+2*x)*x + 2*(2*k+3)*x - 2*x*(2*k+1 +2*x+1)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, Oct 04 2013

MAPLE

with(linalg): M:=matrix(2, 2, [0, 4, 1, 4]): v[0]:=matrix(2, 1, [0, 1]): for n from 1 to 23 do v[n]:=multiply(M, v[n-1]) od: seq(v[n][1, 1], n=0..23);

MATHEMATICA

M = {{0, 4}, {1, 4}} v[1] = {0, 1} v[n_] := v[n] = M.v[n - 1] a = Table[v[n][[1]], {n, 1, 50}]

CROSSREFS

Cf. A009013.

Sequence in context: A081682 A068788 A094013 * A183146 A160564 A075581

Adjacent sequences:  A106565 A106566 A106567 * A106569 A106570 A106571

KEYWORD

nonn,easy,less

AUTHOR

Roger L. Bagula, May 30 2005

EXTENSIONS

Edited by N. J. A. Sloane, Apr 30 2006

Simpler name using o.g.f. by Joerg Arndt, Oct 05 2013

STATUS

approved

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Last modified July 25 14:33 EDT 2017. Contains 289795 sequences.