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%I #22 Apr 18 2017 22:43:38
%S 2,4,5,7,11,13,23,25,47,49,95,97,191,193,383,385,767,769,1535,1537,
%T 3071,3073,6143,6145,12287,12289,24575,24577,49151,49153,98303,98305,
%U 196607,196609,393215,393217,786431,786433,1572863,1572865
%N a(n) = 3*2^floor((n-1)/2) + (-1)^n.
%C Previous name was: a(1)=2 then if n even a(n)=a(n-1)+2 and if n odd a(n)=a(n-2)+a(n-1)-1.
%C This sequence a(n)=A016116(n-1)+A086341(n). Generalization: starting with a(1) even then if n even a(n)=a(n-1)+2 and if n odd a(n)=a(n-2)+a(n-1)-1 you get a new sequence as a(1) increases. But if a(1) is odd, you get always the same sequence with only less values as a(1) increases. If a(1) is even, the sequence difference between two sequences with different but consecutive a(1) is the sequence of powers of 2 = 2,2,4,4,8,8,16,16,32,32,......
%H G. C. Greubel, <a href="/A097581/b097581.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (-1,2,2).
%F From _R. J. Mathar_, Nov 13 2009: (Start)
%F a(n) = -a(n-1) + 2*a(n-2) + 2*a(n-3).
%F G.f.: x*(2+6*x+5*x^2)/((1+x)*(1-2*x^2)). (End)
%e Starting with a(1)=4 the new sequence is 4,6,9,11,19,21,39,41,79,81,159,161
%e The sequence difference between sequence starting with a(1)=4 and the sequence starting with a(1)=2 is 2,2,4,4,8,8,16,16,32,32,64,64,.......
%t LinearRecurrence[{-1,2,2},{2,4,5},40] (* _Harvey P. Dale_, Aug 10 2011 *)
%t Table[3*2^(Floor[(n - 1)/2]) + (-1)^n, {n, 1,50}] (* _G. C. Greubel_, Apr 18 2017 *)
%o (PARI) a(n)=3*2^floor((n-1)/2)+(-1)^n
%Y Cf. A016116, A086341.
%K nonn
%O 1,1
%A _Pierre CAMI_, Sep 20 2004
%E Equation in the comment corrected by _R. J. Mathar_, Nov 13 2009
%E Better name from _Ralf Stephan_, Aug 19 2013