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%I #20 Oct 09 2021 06:46:24
%S 1,2,4,8,18,44,112,288,740,1896,4848,12384,31624,80752,206208,526592,
%T 1344784,3434272,8770368,22397568,57198368,146071744,373034240,
%U 952645120,2432840256,6212924032,15866403584,40519208448,103476899968
%N a(n) = Sum_{k=0..floor(n/4)} C(n-2k,2k) * 2^(n-3k).
%C Binomial transform of 1,1,1,1,3,3,7,7,41,... (g.f. (1-x)(1+x)^2/(1-2x^2-x^4)).
%H Seiichi Manyama, <a href="/A100132/b100132.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4,0,2)
%F G.f.: (1-2x)/((1-2x)^2-2x^4).
%F a(n) = 4*a(n-1) - 4*a(n-2) + 2*a(n-3).
%F a(n) = Sum_{k=0..floor(n/2)} C(n-k, k)2^(n-3k/2)(1+(-1)^k)/2. - _Paul Barry_, Jan 22 2005
%t LinearRecurrence[{4,-4,0,2},{1,2,4,8},30] (* _Harvey P. Dale_, Jun 07 2016 *)
%o (PARI) a(n) = sum(k=0, n\4, binomial(n-2*k, 2*k)*2^(n-3*k)); \\ _Michel Marcus_, Oct 09 2021
%Y Cf. A100131, A100133.
%K easy,nonn
%O 0,2
%A _Paul Barry_, Nov 06 2004
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