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Numbers of the form 2^k or 7*2^k.
3

%I #20 Jan 17 2022 02:47:24

%S 1,2,4,7,8,14,16,28,32,56,64,112,128,224,256,448,512,896,1024,1792,

%T 2048,3584,4096,7168,8192,14336,16384,28672,32768,57344,65536,114688,

%U 131072,229376,262144,458752,524288,917504,1048576,1835008,2097152

%N Numbers of the form 2^k or 7*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+2x^2+3x^3)/(1-2x^2). - _Michael Somos_, Nov 05 2002

%F Sum_{n>=0} 1/a(n) = 16/7. - _Amiram Eldar_, Jan 17 2022

%t Sort[Flatten[{#,7#}&/@(2^Range[0,21])]] (* or *) CoefficientList[Series[ (1+2x+2x^2+3x^3)/(1-2x^2),{x,0,50}],x] (* _Harvey P. Dale_, Apr 23 2011 *)

%o (PARI) a(n)=if(n<0,0,if(n<2,2^n,if(n%2,7/2,2)*2^(n\2)))

%Y Cf. A000079, A005009, A029744, A029748.

%K nonn

%O 0,2

%A _N. J. A. Sloane_.