A132723 - OEIS

%I #14 Feb 15 2021 01:59:58

%S 3,4,4,0,-8,-16,-16,0,32,64,64,0,-128,-256,-256,0,512,1024,1024,0,

%T -2048,-4096,-4096,0,8192,16384,16384,0,-32768,-65536,-65536,0,131072,

%U 262144,262144,0,-524288,-1048576,-1048576

%N Binomial transform of A132429.

%C Sequence is identical to its fourth differences.

%H G. C. Greubel, <a href="/A132723/b132723.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 (2,-2).

%F a(n) = 4*a(n-1) - 6*a(n-2) + 4*a(n-3), n positive. For a(0)=3,a(1)=a(2)=4,a(3)=0.

%F From _R. J. Mathar_, Apr 02 2008: (Start)

%F O.g.f.: 1 + 2/(1 -2*x +2*x^2).

%F a(n) = 2*a(n-1) - 2*a(n-2) if n>2. (End)

%F E.g.f.: 1 + 2*sqrt(2)*exp(x)*sin(x + Pi/4). - _G. C. Greubel_, Feb 14 2021

%t Join[{3},LinearRecurrence[{2,-2},{4,4},50]] (* _Harvey P. Dale_, Mar 06 2014 *)

%t Table[If[n<2, n+3, 2*((1+I)^(n-1) + (1-I)^(n-1))], {n,0,40}] (* _G. C. Greubel_, Feb 14 2021 *)

%o (Sage)

%o def A132723(n): return n+3 if (n<2) else 2*( (1+i)^(n-1) + (1-i)^(n-1) )

%o [A132723(n) for n in (0..40)] # _G. C. Greubel_, Feb 14 2021

%o (Magma) [3] cat [n le 2 select 4 else 2*(Self(n-1) - Self(n-2)): n in [1..40]]; // _G. C. Greubel_, Feb 14 2021

%K sign

%O 0,1

%A _Paul Curtz_, Nov 16 2007

%E More terms from _R. J. Mathar_, Apr 02 2008