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Expansion of (1+4x-24x^2)/((1-4x)(1+4x)).
0

%I #8 Dec 14 2019 16:16:45

%S 1,4,-8,64,-128,1024,-2048,16384,-32768,262144,-524288,4194304,

%T -8388608,67108864,-134217728,1073741824,-2147483648,17179869184,

%U -34359738368,274877906944,-549755813888,4398046511104,-8796093022208,70368744177664

%N Expansion of (1+4x-24x^2)/((1-4x)(1+4x)).

%C a(0)=1, a(2n-1)=k^(2n-1), a(2n)=(2-k)k^(2n-1), k=4; G.f.: (1+kx+(2-2k)kx^2)/((1-kx)(1+kx)), k=4.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,16).

%F a(n)=4^n/4+(-3)(-4)^n/4+6*0^n/4

%t LinearRecurrence[{0,16},{1,4,-8},30] (* _Harvey P. Dale_, Dec 14 2019 *)

%K easy,sign

%O 0,2

%A _Paul Barry_, Dec 19 2003