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%I A166752 #13 Sep 08 2022 08:45:48
%S A166752 1,1,3,1,11,1,43,1,171,1,683,1,2731,1,10923,1,43691,1,174763,1,699051,
%T A166752 1,2796203,1,11184811,1,44739243,1,178956971,1,715827883,1,2863311531,
%U A166752 1,11453246123,1,45812984491,1,183251937963,1,733007751851,1
%N A166752 Interleave A007583 and A000012.
%C A166752 Partial sums are A166753.
%H A166752 G. C. Greubel, <a href="/A166752/b166752.txt">Table of n, a(n) for n = 0..1000</a>
%H A166752 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0,5,0,-4).
%F A166752 G.f.: (1+x-2*x^2-4*x^3)/(1-5*x^2+4*x^4).
%F A166752 G.f.: (1+x)/(1-5*x^2+4*x^4) - 2*x^2*(1+2*x)/(1-5*x^2+4*x^4).
%F A166752 a(n) = (4*4^floor(n/2)-1)/3 - 2*floor(2^n/3).
%F A166752 a(n) = 4*4^floor(n/2)/3 - 2*2^n/3 - (-1)^n/3 + 2/3.
%F A166752 a(n) = A002450(floor(n/2)+1) - 2*A000975(n-1).
%t A166752 LinearRecurrence[{0, 5, 0, -4}, {1, 1, 3, 1}, 100] (* _G. C. Greubel_, May 24 2016 *)
%o A166752 (PARI) x='x+O('x^50); Vec((1+x-2*x^2-4*x^3)/(1-5*x^2+4*x^4)) \\ _G. C. Greubel_, Oct 10 2017
%o A166752 (Magma) [(4*4^Floor(n/2)-1)/3 - 2*Floor(2^n/3): n in [0..25]]; // _G. C. Greubel_, Oct 10 2017
%K A166752 easy,nonn
%O A166752 0,3
%A A166752 _Paul Barry_, Oct 21 2009

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