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a(n) = 2*a(n-1) if n odd else 2*a(n-1) + 6.
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%I #19 Aug 26 2024 19:07:25

%S 0,6,12,30,60,126,252,510,1020,2046,4092,8190,16380,32766,65532,

%T 131070,262140,524286,1048572,2097150,4194300,8388606,16777212,

%U 33554430,67108860,134217726,268435452,536870910

%N a(n) = 2*a(n-1) if n odd else 2*a(n-1) + 6.

%H Vincenzo Librandi, <a href="/A014131/b014131.txt">Table of n, a(n) for n = 0..1000</a>

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2, 1, -2).

%F a(n) = 3*A026644(n), n > 0. [moved from A020988 by _R. J. Mathar_, Oct 21 2008]

%F From _R. J. Mathar_, Oct 21 2008: (Start)

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

%F a(n) = 2^(n+2) - 3 - (-1)^n. (End)

%t Table[2^(n+2)-3-(-1)^n,{n,0,40}] (* or *) CoefficientList[Series[6x/((1-2x)(1-x)(1+x)),{x,0,30}],x] (* _Vincenzo Librandi_, Apr 03 2012 *)

%t nxt[{n_,a_}]:={n+1,If[EvenQ[n],2a,2a+6]}; NestList[nxt,{1,0},30][[;;,2]] (* or *) LinearRecurrence[ {2,1,-2},{0,6,12},30] (* _Harvey P. Dale_, Aug 26 2024 *)

%o (Magma) [2^(n+2)-3-(-1)^n: n in [0..30]]; // _Vincenzo Librandi_, Apr 03 2012

%Y Cf. A000975.

%K nonn

%O 0,2

%A _N. J. A. Sloane_