

A106568


Expansion of 4*x/(14*x4*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
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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 nanacci 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
From Philippe Deléham, Sep 19 2009: (Start)
a(n) = 4*a(n1) + 4*a(n2) for n > 2; a(0) = 0, a(1)=4.
G.f.: 4x/(14x4x^2). (End)
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[n1]) 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



