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%I #31 Jan 21 2022 05:04:50
%S 1,2,8,5,16,10,32,20,64,40,128,80,256,160,512,320,1024,640,2048,1280,
%T 4096,2560,8192,5120,16384,10240,32768,20480,65536,40960,131072,81920,
%U 262144,163840,524288,327680,1048576,655360,2097152,1310720,4194304
%N Expansion of (1 + 2x + 6x^2 + x^3)/(1 - 2x^2).
%C Note that 4 is the only power of 2 not here. All terms are either 2^k or 5*2^k.
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (0,2).
%F G.f.: (1 + 2x + 6x^2 + x^3)/(1 - 2x^2).
%F Sum_{n>=1} 1/a(n) = 43/20. - _Amiram Eldar_, Jan 21 2022
%t LinearRecurrence[{0,2},{1,2,8,5},50] (* or *) With[{nn=20},Join[{1,2}, Riffle[ 8*2^Range[0,nn],5 2^Range[0,nn]]]] (* _Harvey P. Dale_, Sep 28 2016 *)
%o (PARI) a(n)=if(n<2,1+max(-1,n),2^(n\2)*if(n%2,5/2,4))
%Y Cf. A094958 (numbers of the form 2^k or 5*2^k).
%K nonn,easy
%O 1,2
%A _N. J. A. Sloane_
%E Edited by _T. D. Noe_, Nov 12 2010
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