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%I #8 Jun 13 2015 00:53:28
%S 1,1,1,-3,-7,-19,-39,-83,-167,-339,-679,-1363,-2727,-5459,-10919,
%T -21843,-43687,-87379,-174759,-349523,-699047,-1398099,-2796199,
%U -5592403,-11184807,-22369619,-44739239,-89478483,-178956967,-357913939,-715827879,-1431655763
%N a(0)=a(1)=1, a(n) = 2*a(n-1)- A010686(n), n>1.
%C The sequence in the first row and successive differences in followup rows defines the array
%C 1, 1, 1, -3, -7, -19, -39, -83, -167, -339,..
%C 0, 0, -4, -4, -12, -20, -44, -84, -172, -340,..
%C 0, -4, 0, -8, -8, -24, -40, -88, -168, -344,..
%C -4, 4, -8, 0, -16, -16, -48, -80, -176, -336,..
%C 8, -12, 8, -16, 0, -32, -32, -96, -160, -352, ..
%C The first two subdiagonals show essentially the powers of 2.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (2,1,-2).
%F a(n) = 3+ 2*( (-1)^n-2^n )/3 = 3-A078008(n+1), n>0. [R. J. Mathar, Jun 30 2010]
%F a(n+2)-a(n)= A154589(n+2) = -2^(n+1), n>0.
%F a(n)= 2*a(n-1)+a(n-2)-2*a(n-3), n>3.
%F G.f.: (-x-2*x^2-4*x^3+1)/( (1-x)*(1-2*x)*(1+x) ).
%F a(n) + A173078(n) = 2^n.
%F a(n) - a(n-1) = -4*A001045(n-2) = -A097074(n-1), n>1.
%K easy,sign
%O 0,4
%A _Paul Curtz_, Feb 10 2010
%E Edited and extended by _R. J. Mathar_, Jun 30 2010
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