%I #14 Mar 08 2021 12:48:55

%S 0,1,-2,4,-24,16,-224,64,-1920,256,-15872,1024,-129024,4096,-1040384,

%T 16384,-8355840,65536,-66977792,262144,-536346624,1048576,-4292870144,

%U 4194304,-34351349760,16777216,-274844352512,67108864,-2198889037824,268435456,-17591649173504,1073741824

%N Expansion of x(1-4x)/((1-2x)(1-8x^2)).

%C Let A=[1,2,1;2,0,-2;1,-2,1] the 3 X 3 symmetric Krawtchouk matrix. Than a(n) is the 1,3 element of A^n.

%D P. Feinsilver and J. Kocik, Krawtchouk matrices from classical and quantum walks, Contemporary Mathematics, 287 2001, pp. 83-96.

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (2,8,-16).

%F a(n)=2^(n-1)-2^(3(n-1)/2)(1+(-1)^n)/sqrt(2); a(n)=2a(n-1)+8a(n-2)-16a(n-3).

%F a(n) = (-2)^(n-1)*A094024(n-1). - _R. J. Mathar_, Mar 08 2021

%t CoefficientList[Series[x (1-4x)/((1-2x)(1-8x^2)),{x,0,40}],x] (* or *) LinearRecurrence[{2,8,-16},{0,1,-2},40] (* _Harvey P. Dale_, Jun 30 2011 *)

%Y Cf. A098655, A098657.

%K easy,sign

%O 0,3

%A _Paul Barry_, Sep 19 2004