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A168642 a(n) = (8*2^n + (-1)^n)/3 for n > 0; a(0) = 1. 3

%I

%S 1,5,11,21,43,85,171,341,683,1365,2731,5461,10923,21845,43691,87381,

%T 174763,349525,699051,1398101,2796203,5592405,11184811,22369621,

%U 44739243,89478485,178956971,357913941,715827883,1431655765,2863311531

%N a(n) = (8*2^n + (-1)^n)/3 for n > 0; a(0) = 1.

%C a(n) = A001045(n+3) for n > 0.

%C First differences of A085278.

%H Vincenzo Librandi, <a href="/A168642/b168642.txt">Table of n, a(n) for n = 0..200</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,2).

%F a(n) = a(n-1) + 2*a(n-2) for n > 2; a(0) = 1, a(1) = 5, a(2) = 11.

%F G.f.: (1 + 2*x)^2/((1+x)*(1-2*x)).

%F E.g.f.: (1/3)*(8*exp(2*x) + exp(-x)). - _G. C. Greubel_, Jul 28 2016

%t Table[(8*2^n + (-1)^n)/3, {n,0,50}] (* or *) LinearRecurrence[{1,2}, {1,5}, 25] (* _G. C. Greubel_, Jul 28 2016 *)

%o (MAGMA) [1] cat [ (8*2^n+(-1)^n)/3: n in [1..30] ];

%o (PARI) a(n)=([0,1; 2,1]^n*[1;5])[1,1] \\ _Charles R Greathouse IV_, Jul 29 2016

%Y Cf. A001045 (Jacobsthal sequence), A085278 (expansion of (1+2x)^2/((1-x^2)(1-2x)).

%K nonn,easy

%O 0,2

%A _Klaus Brockhaus_, Dec 01 2009

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Last modified May 28 13:20 EDT 2020. Contains 334683 sequences. (Running on oeis4.)