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Expansion of (1-5x)/(1-8x+4x^2).
1

%I #28 Jan 01 2024 08:34:18

%S 1,3,20,148,1104,8240,61504,459072,3426560,25576192,190903296,

%T 1424921600,10635759616,79386390528,592548085760,4422839123968,

%U 33012520648704,246408808693760,1839220386955264,13728127860867072

%N Expansion of (1-5x)/(1-8x+4x^2).

%C Hankel transform of 1,1,4,18,88,.... (see A081671).

%H Vincenzo Librandi, <a href="/A154627/b154627.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 (8,-4).

%F a(n) = 8*a(n-1) - 4*a(n-2), n > 1; a(0)=1, a(1)=3. [_Philippe Deléham_, Feb 02 2009]

%p A[0]:= 1: A[1]:= 3:

%p for n from 2 to 100 do A[n]:= 8*A[n-1]-4*A[n-2] od:

%p seq(A[n],n=0..100); # _Robert Israel_, Aug 10 2014

%t LinearRecurrence[{8,-4},{1,3},20] (* _Harvey P. Dale_, Aug 10 2014 *)

%t CoefficientList[Series[(1 - 5 x)/(1 - 8 x + 4 x^2), {x, 0, 50}], x] (* _Vincenzo Librandi_, Aug 10 2014 *)

%o (PARI) Vec((1-5*x)/(1-8*x+4*x^2)+O(x^50)) \\ _Michel Marcus_, Aug 10 2014

%K easy,nonn

%O 0,2

%A _Paul Barry_, Jan 13 2009