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%I #26 Sep 08 2022 08:45:35
%S 2,1,3,-1,7,-9,23,-41,87,-169,343,-681,1367,-2729,5463,-10921,21847,
%T -43689,87383,-174761,349527,-699049,1398103,-2796201,5592407,
%U -11184809,22369623,-44739241,89478487,-178956969,357913943
%N a(n) = (5 + (-2)^n)/3.
%C Inverse binomial transform of A048573.
%C This is an example of the case k=-1 of sequences with recurrences a(n) = k*a(n-1) + (k+3)*a(n-2) - (2*k+2)*a(n-3).
%C The case k=1 is covered, for example, by A097163, A135520, A136326, A136336, or A137208.
%C Sequences with k=2 are A094554 and A094555.
%C Sequences with k=3 are A084175, A108924, and A139818.
%H Vincenzo Librandi, <a href="/A140966/b140966.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-1,2).
%F a(n) = -a(n-1) + 2*a(n-2).
%F G.f.: (2+3*x)/((1-x)*(1+2*x)).
%F a(n+1) - a(n) = (-1)^(n+1)*A000079(n).
%F a(n+3) = (-1)^n*A083582(n).
%F a(n+1) - 2*a(n) = -a(n+2).
%F a(n+1) - 3*a(n) = 5*(-1)^(n+1)*A078008(n) = (-1)^(n+1)*A001045(n-1).
%F a(2n+3) = -A083584(n), a(2n) = A163834(n). - _Philippe Deléham_, Feb 24 2014
%t (5+(-2)^Range[0,30])/3 (* or *) LinearRecurrence[{-1,2},{2,1},40] (* _Harvey P. Dale_, Apr 23 2019 *)
%o (Magma) [( 5+(-2)^n)/3: n in [0..35]]; // _Vincenzo Librandi_, Jul 05 2011
%o (PARI) a(n)=(5+(-2)^n)/3 \\ _Charles R Greathouse IV_, Oct 07 2015
%K sign,easy
%O 0,1
%A _Paul Curtz_, Jul 27 2008
%E Definition simplified by _R. J. Mathar_, Sep 11 2009
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