%I #23 Sep 08 2022 08:45:50
%S 0,1,3,-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,-715827881
%N Inverse binomial transform of A084640.
%C a(n) and differences are
%C 0, 1, 3, -1, 7, -9,
%C 1, 2, -4, 8, -16, 32, =(-1)^(n+1) * A171449(n),
%C 1, -6, 12, -24, 48, -96,
%C -7, 18, -36, 72, -144, 288,
%C 25, -54, 108, -216, 432, -864,
%C Vertical: 1) 0 followed with A168589(n).
%C 2) (-1 followed with A008776(n) ) signed. See A025192(n).
%C Main diagonal: see A167747(1+n). - _Paul Curtz_, Jun 16 2011
%H Vincenzo Librandi, <a href="/A171501/b171501.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) = A140966(n), n>0.
%F G.f.: x*(1+4*x) / ( (1+2*x)*(1-x) ). - _R. J. Mathar_, Jun 14 2011
%F a(1+n)= (-1)^(1+n) * A001045(1+n) + 2. - _Paul Curtz_, Jun 16 2011
%t CoefficientList[Series[x*(1 + 4*x)/((1 + 2*x)*(1 - x)), {x, 0, 30}], x]
%t LinearRecurrence[{-1,2},{0,1,3},40] (* _Harvey P. Dale_, Jan 14 2020 *)
%o (Magma) I:=[0, 1, 3]; [n le 3 select I[n] else -Self(n-1) + 2*Self(n-2): n in [1..40]]; // _Vincenzo Librandi_, Oct 18 2012
%K easy,sign
%O 0,3
%A _Paul Curtz_, Dec 10 2009
%E Mathematica program by _Olivier GĂ©rard_, Jul 06 2011