%I #8 Mar 04 2018 08:20:28
%S 0,1,2,3,4,5,7,8,9,15,16,17,31,32,33,63,64,65,127,128,129,255,256,257,
%T 511,512,513,1023,1024,1025,2047,2048,2049,4095,4096,4097,8191,8192,
%U 8193,16383,16384,16385,32767,32768,32769,65535,65536,65537,131071
%N Union of sequences 2^k-1, 2^k and 2^k+1.
%C Subsequence of A107686.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (-1,-1,2,2,2).
%F a(n) = if n<=2 then n else 2^(floor(n/3)+1) + n mod 3 - 1. - _Reinhard Zumkeller_, Jun 05 2005
%F G.f.:-x*(1+3*x+6*x^2+7*x^3+6*x^4+4*x^5+2*x^6)/((2*x^3-1)*(x^2+x+1)) [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 12 2009]
%t Flatten[{#-1,#,#+1}&/@(2^Range[0,20])]//Union (* _Harvey P. Dale_, Oct 06 2017 *)
%Y Cf. A000225, A000079, A000051.
%K nonn
%O 0,3
%A _Reinhard Zumkeller_, May 20 2005
%E Description corrected by Henrik Lundquist, Jun 06 2005
|