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a(n) = 4*a(n-1) - 8*a(n-2) with a(0) = a(1) = 1.
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%I #11 May 19 2023 14:18:50

%S 1,1,-4,-24,-64,-64,256,1536,4096,4096,-16384,-98304,-262144,-262144,

%T 1048576,6291456,16777216,16777216,-67108864,-402653184,-1073741824,

%U -1073741824,4294967296,25769803776,68719476736,68719476736,-274877906944,-1649267441664,-4398046511104

%N a(n) = 4*a(n-1) - 8*a(n-2) with a(0) = a(1) = 1.

%D Paul J. Nahin, An Imaginary Tale: The Story of sqrt(-1), Princeton University Press, Princeton, NJ. 1998, pp. 94-96.

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-8).

%F a(n) = 2^(3*n/2-1)*(2*cos(n*Pi/4) - sin(n*Pi/4)).

%F O.g.f.: (1 - 3*x)/(1 - 4*x + 8*x^2).

%F E.g.f.: exp(2*x)*(2*cos(2*x) - sin(2*x))/2.

%F a(n+1) = a(n) iff n is a multiple of 4.

%t LinearRecurrence[{4,-8},{1,1},29]

%Y Cf. A000045, A008586, A088137, A088138.

%K sign,easy

%O 0,3

%A _Stefano Spezia_, May 19 2023