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Expansion of (1 -2*x +4*x^2 -22*x^3 +6*x^4 +268*x^5 -854*x^6 +3596*x^7 -3100*x^8)/((1 -2*x)/(1 -2*x -4*x^2)).
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%I #39 Sep 08 2022 08:45:23

%S 1,2,12,18,62,420,682,5828,16852,61952,201184,669920,2184064,7126784,

%T 23147776,75118592,243460096,788658176,2553683968,8267055104,

%U 26758955008,86606348288,280288952320,907084169216,2935485890560

%N Expansion of (1 -2*x +4*x^2 -22*x^3 +6*x^4 +268*x^5 -854*x^6 +3596*x^7 -3100*x^8)/((1 -2*x)/(1 -2*x -4*x^2)).

%H Vincenzo Librandi, <a href="/A115109/b115109.txt">Table of n, a(n) for n = 0..500</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,-8).

%F G.f.: -(3100*x^8 -3596*x^7 +854*x^6 -268*x^5 -6*x^4 +22*x^3 -4*x^2 +2*x -1) / ((2*x -1)*(4*x^2 +2*x -1)). - _Colin Barker_, Mar 15 2013

%F a(n) = +4*a(n-1) -8*a(n-3). - _Colin Barker_, Mar 15 2013

%t Join[{1, 2, 12, 18, 62, 420}, {LinearRecurrence[{4, 0, -8}, {682, 5828, 16852}, 20]}] (* _Bruno Berselli_, Mar 15 2013 *)

%o (Magma) I:=[1, 2, 12, 18, 62, 420, 682, 5828, 16852]; [n le 9 select I[n] else 4*Self(n-1) - 8*Self(n-3): n in [1..30]]; // _Vincenzo Librandi_, Mar 18 2013

%K nonn,easy

%O 0,2

%A _Roger L. Bagula_, Mar 03 2006

%E Definition rewritten using Colin Barker's g.f. by _Bruno Berselli_, Mar 15 2013