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a(0)=2, a(1)=8, a(n) = a(n-1) + 2*a(n-2).
2

%I #33 May 26 2024 15:22:38

%S 2,8,12,28,52,108,212,428,852,1708,3412,6828,13652,27308,54612,109228,

%T 218452,436908,873812,1747628,3495252,6990508,13981012,27962028,

%U 55924052,111848108,223696212,447392428,894784852,1789569708,3579139412,7158278828

%N a(0)=2, a(1)=8, a(n) = a(n-1) + 2*a(n-2).

%C Essentially 2 * A084214.

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

%F From _R. J. Mathar_, Jun 14 2011: (Start)

%F G.f.: (2+6*x)/( (1+x)*(1-2*x) ).

%F a(n) = 2*A084214(n+1). (End)

%F a(n) = (4*(-1)^n + 5*2^n)/3. - _Harvey P. Dale_, Sep 02 2016

%F a(n) = 2*a(n-1) - 4*(-1)^n. - _Paul Curtz_, May 26 2024

%t LinearRecurrence[{1,2},{2,8},40] (* or *) Table[(4(-1)^x+5*2^x)/3,{x,40}] (* _Harvey P. Dale_, Sep 02 2016 *)

%Y Cf. A078008, A014551.

%Y Cf. A010709.

%K nonn,easy

%O 0,1

%A _Roger L. Bagula_, Mar 02 2006

%E Edited by _N. J. A. Sloane_, Dec 04 2006