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a(n) = floor(2^(n-2)*3*n).
5

%I #43 Sep 08 2022 08:45:30

%S 1,6,18,48,120,288,672,1536,3456,7680,16896,36864,79872,172032,368640,

%T 786432,1671168,3538944,7471104,15728640,33030144,69206016,144703488,

%U 301989888,629145600,1308622848,2717908992,5637144576

%N a(n) = floor(2^(n-2)*3*n).

%C Also row sums of triangle A249111. - _Reinhard Zumkeller_, Nov 15 2014

%H Vincenzo Librandi, <a href="/A128543/b128543.txt">Table of n, a(n) for n = 1..1000</a>

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

%F Binomial transform of A007310 (assuming offset 0 in both sequences).

%F Row sums of triangle A134239. - _Gary W. Adamson_, Oct 14 2007

%F a(n) = 3*n*2^(n-2) for n>1. - _R. J. Mathar_, Oct 25 2011

%F From _Colin Barker_, Mar 22 2012: (Start)

%F a(n) = 4*a(n-1) - 4*a(n-2) for n>3.

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

%t CoefficientList[Series[(1+2*x-2*x^2)/(1-2*x)^2,{x,0,40}],x] (* _Vincenzo Librandi_, Jun 28 2012 *)

%o (Magma) I:=[1, 6, 18]; [n le 3 select I[n] else 4*Self(n-1)-4*Self(n-2): n in [1..40]]; // _Vincenzo Librandi_, Jun 28 2012

%o (Haskell)

%o a128543 = sum . a134239_row . subtract 1

%o -- _Reinhard Zumkeller_, Nov 15 2014

%o (PARI) a(n)=3*n*2^n\4 \\ _Charles R Greathouse IV_, Oct 07 2015

%o (Sage) [1]+[3*n*2^(n-2) for n in (2..40)] # _G. C. Greubel_, Jul 11 2019

%o (GAP) Concatenation([1], List([2..40], n-> 3*n*2^(n-2))); # _G. C. Greubel_, Jul 11 2019

%Y Cf. A007310, A134239, A249111.

%K nonn,easy

%O 1,2

%A _Gary W. Adamson_, Mar 10 2007

%E Definition corrected by _M. F. Hasler_, Nov 05 2014