A180222 a(n) = 4*a(n-1) + 8*a(n-2), with a(1)=0 and a(2)=1.

0, 1, 4, 24, 128, 704, 3840, 20992, 114688, 626688, 3424256, 18710528, 102236160, 558628864, 3052404736, 16678649856, 91133837312, 497964548096, 2720928890880, 14867431948288, 81237158920192, 443888091267072, 2425449636429824, 13252903275855872

Offset: 1

Author

Vladimir Joseph Stephan Orlovsky, Jan 16 2011

Keywords

• nonn
• easy

Links

• Nathaniel Johnston, Table of n, a(n) for n = 1..500
• Index entries for linear recurrences with constant coefficients, signature (4,8).

Programs

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

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 *)

PARI

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

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..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