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%I #25 Feb 08 2022 22:05:09
%S 1,4,2,8,4,16,8,32,16,64,32,128,64,256,128,512,256,1024,512,2048,1024,
%T 4096,2048,8192,4096,16384,8192,32768,16384,65536,32768,131072,65536,
%U 262144,131072,524288,262144,1048576,524288,2097152,1048576,4194304
%N (1, 2, 4, 8, ...) interleaved with (4, 8, 16, 32, ...).
%C Partial sums are in A079360. a(n) = A076736(n+5). - _Klaus Brockhaus_, Jul 27 2009
%H G. C. Greubel, <a href="/A143095/b143095.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,2).
%F Inverse binomial transform of A048655: (1, 5, 11, 27, 65, 157, ...).
%F a(n) = A135530(n+1). - _R. J. Mathar_, Aug 02 2008
%F From _Klaus Brockhaus_, Jul 27 2009: (Start)
%F a(n) = (5 - 3*(-1)^n) * 2^((2*n-1+(-1)^n)/4)/2.
%F a(n) = 2*a(n-2) for n > 1; a(0) = 1, a(1) = 4.
%F G.f.: (1+4*x)/(1-2*x^2). (End)
%F a(n+3) = a(n+2)*a(n+1)/a(n). - _Reinhard Zumkeller_, Mar 04 2011
%p seq(coeff(series((1+4*x)/(1-2*x^2), x, n+1), x, n), n = 0..45); # _G. C. Greubel_, Mar 13 2020
%t nn=30;With[{p=2^Range[0,nn]},Riffle[Take[p,nn-2],Drop[p,2]]] (* _Harvey P. Dale_, Oct 03 2011 *)
%o (PARI) for(n=0, 41, print1((5-3*(-1)^n)*2^(1/4*(2*n-1+(-1)^n))/2, ",")) \\ _Klaus Brockhaus_, Jul 27 2009
%o (Maxima) A143095(n):=(5-3*(-1)^n)*2^(1/4*(2*n-1+(-1)^n))/2$
%o makelist(A143095(n),n,0,30); /* _Martin Ettl_, Nov 03 2012 */
%o (Sage) [(5 -3*(-1)^n)*2^((2*n-1+(-1)^n)/4)/2 for n in (0..45)] # _G. C. Greubel_, Mar 13 2020
%Y Cf. A048655.
%K nonn,easy
%O 0,2
%A _Gary W. Adamson_ & _Roger L. Bagula_, Jul 23 2008
%E More terms from _Klaus Brockhaus_, Jul 27 2009
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