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a(n) = (4^n + 8)/3.
4

%I #24 Dec 05 2023 14:38:38

%S 3,4,8,24,88,344,1368,5464,21848,87384,349528,1398104,5592408,

%T 22369624,89478488,357913944,1431655768,5726623064,22906492248,

%U 91625968984,366503875928,1466015503704,5864062014808,23456248059224,93824992236888,375299968947544

%N a(n) = (4^n + 8)/3.

%H Vincenzo Librandi, <a href="/A155701/b155701.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (5,-4).

%F a(n) = 3 + A002450(n).

%F a(n) = 5*a(n-1) - 4*a(n-2) = 4*a(n-1) - 8.

%F a(n) = A154879(2n) = A154890(2n).

%F a(n+1) - a(n) = A000302(n).

%F a(n+1) = 4*A047849(n) = 4*A078008(2n).

%F G.f.: (3-11*x)/((4*x-1)*(x-1)). - _R. J. Mathar_, Jul 23 2009

%p A155701 := proc(n) (4^n+8)/3 ; end: seq(A155701(n),n=0..80) ; # _R. J. Mathar_, Jul 23 2009

%t A155701[n_]:=(4^n+8)/3;Array[A155701,50,0] (* _Paolo Xausa_, Dec 05 2023 *)

%o (Magma) [(4^n+8)/3: n in [0..35]]; // _Vincenzo Librandi_, Jul 24 2011

%K nonn,easy

%O 0,1

%A _Paul Curtz_, Jan 25 2009

%E Edited and extended by _R. J. Mathar_, Jul 23 2009