A053565 - OEIS

%I #23 Sep 08 2022 08:45:00

%S -2,-1,4,20,64,176,448,1088,2560,5888,13312,29696,65536,143360,311296,

%T 671744,1441792,3080192,6553600,13893632,29360128,61865984,130023424,

%U 272629760,570425344,1191182336,2483027968,5167382528,10737418240

%N a(n) = 2^(n-1)*(3*n-4).

%D A. H. Beiler, Recreations in the Theory of Numbers, Dover, N.Y., 1964, pp. 189, 194-196.

%H Vincenzo Librandi, <a href="/A053565/b053565.txt">Table of n, a(n) for n = 0..2000</a>

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

%F a(n) = 4*a(n-1) - 4*a(n-2), with a(0) = -2, a(1) = -1.

%F G.f.: -(2-7*x)/(1-2*x)^2. - _Colin Barker_, Apr 07 2012

%F E.g.f.: (3*x - 2)*exp(2*x). - _G. C. Greubel_, May 16 2019

%t Table[2^(n-1)*(3*n-4), {n,0,30}] (* _G. C. Greubel_, May 16 2019 *)

%o (Magma) [2^(n-1)*(3*n-4): n in [0..30]]; // _Vincenzo Librandi_, Sep 26 2011

%o (PARI) vector(30, n, n--; 2^(n-1)*(3*n-4)) \\ _G. C. Greubel_, May 16 2019

%o (Sage) [2^(n-1)*(3*n-4) for n in (0..30)] # _G. C. Greubel_, May 16 2019

%o (GAP) List([0..30], n-> 2^(n-1)*(3*n-4)) # _G. C. Greubel_, May 16 2019

%Y Cf. A023444.

%Y Cf. A027992, A048496.

%K sign,easy

%O 0,1

%A _Barry E. Williams_, Jan 17 2000