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A140966 a(n) = (5 + (-2)^n)/3.

%I A140966 #31 Jul 27 2024 18:35:53
%S A140966 2,1,3,-1,7,-9,23,-41,87,-169,343,-681,1367,-2729,5463,-10921,21847,
%T A140966 -43689,87383,-174761,349527,-699049,1398103,-2796201,5592407,
%U A140966 -11184809,22369623,-44739241,89478487,-178956969,357913943,-715827881,1431655767,-2863311529,5726623063
%N A140966 a(n) = (5 + (-2)^n)/3.
%C A140966 Inverse binomial transform of A048573.
%C A140966 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 A140966 The case k=1 is covered, for example, by A097163, A135520, A136326, A136336, or A137208.
%C A140966 Sequences with k=2 are A094554 and A094555.
%C A140966 Sequences with k=3 are A084175, A108924, and A139818.
%H A140966 Vincenzo Librandi, <a href="/A140966/b140966.txt">Table of n, a(n) for n = 0..1000</a>
%H A140966 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (-1,2).
%F A140966 a(n) = -a(n-1) + 2*a(n-2).
%F A140966 G.f.: (2+3*x)/((1-x)*(1+2*x)).
%F A140966 a(n+1) - a(n) = (-1)^(n+1)*A000079(n).
%F A140966 a(n+3) = (-1)^n*A083582(n).
%F A140966 a(n+1) - 2*a(n) = -a(n+2).
%F A140966 a(n+1) - 3*a(n) = 5*(-1)^(n+1)*A078008(n) = (-1)^(n+1)*A001045(n-1).
%F A140966 a(2n+3) = -A083584(n), a(2n) = A163834(n). - _Philippe Deléham_, Feb 24 2014
%F A140966 E.g.f.: (5*exp(x) + exp(-2*x))/3. - _Stefano Spezia_, Jul 27 2024
%t A140966 (5+(-2)^Range[0,30])/3 (* or *) LinearRecurrence[{-1,2},{2,1},40] (* _Harvey P. Dale_, Apr 23 2019 *)
%o A140966 (Magma) [( 5+(-2)^n)/3: n in [0..35]]; // _Vincenzo Librandi_, Jul 05 2011
%o A140966 (PARI) a(n)=(5+(-2)^n)/3 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y A140966 Cf. A048573.
%Y A140966 Cf. A097163, A135520, A136326, A136336, A137208.
%Y A140966 Cf. A094554, A094555.
%Y A140966 Cf. A084175, A108924, A139818.
%Y A140966 Cf. A000079, A001045, A078008, A083582, A083584, A163834.
%K A140966 sign,easy
%O A140966 0,1
%A A140966 _Paul Curtz_, Jul 27 2008
%E A140966 Definition simplified by _R. J. Mathar_, Sep 11 2009