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A180222 a(n) = 4*a(n-1) + 8*a(n-2), with a(1)=0 and a(2)=1. 14
0, 1, 4, 24, 128, 704, 3840, 20992, 114688, 626688, 3424256, 18710528, 102236160, 558628864, 3052404736, 16678649856, 91133837312, 497964548096, 2720928890880, 14867431948288, 81237158920192, 443888091267072, 2425449636429824, 13252903275855872 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Nathaniel Johnston, Table of n, a(n) for n = 1..500

Index entries for linear recurrences with constant coefficients, signature (4,8).

FORMULA

a(n) = 2^(n-3)*((1+sqrt(3))^(n-1)-(1-sqrt(3))^(n-1))/sqrt(3). - Rolf Pleisch, May 14 2011

a(n) = (-1)^n*A174443(n-1). - Nathaniel Johnston, May 14 2011

G.f.: x^2/(1-4*x-8*x^2).

a(n+2) = Sum_{k, 0<=k<=n} A201947(n,k)*3^(n-k) . - Philippe Deléham, Dec 07 2011

a(n+2) = 2^n*A002605(n+1). - R. J. Mathar, May 07 2019

MATHEMATICA

Join[{a=0, b=1}, Table[c=4*b+8*a; a=b; b=c, {n, 100}]]

LinearRecurrence[{4, 8}, {0, 1}, 30] (* G. C. Greubel, Jan 16 2018 *)

PROG

(PARI) concat(0, Vec(1/(1-4*x-8*x^2)+O(x^98))) \\ Charles R Greathouse IV, Dec 07 2011

(MAGMA) I:=[0, 1]; [n le 2 select I[n] else 4*Self(n-1) + 8*Self(n-2): n in [1..30]]; // G. C. Greubel, Jan 16 2018

CROSSREFS

Sequence in context: A103455 A289715 A174443 * A192070 A048180 A057391

Adjacent sequences:  A180219 A180220 A180221 * A180223 A180224 A180225

KEYWORD

nonn,easy

AUTHOR

Vladimir Joseph Stephan Orlovsky, Jan 16 2011

STATUS

approved

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Last modified October 17 15:01 EDT 2019. Contains 328116 sequences. (Running on oeis4.)