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%I #21 Aug 20 2022 13:38:54
%S -1,4,2,10,14,34,62,130,254,514,1022,2050,4094,8194,16382,32770,65534,
%T 131074,262142,524290,1048574,2097154,4194302,8388610,16777214,
%U 33554434,67108862,134217730,268435454,536870914,1073741822,2147483650,4294967294,8589934594,17179869182,34359738370
%N a(n) = a(n-1) + 2a(n-2).
%C First differences of A014551. - _Reinhard Zumkeller_, Jan 02 2013
%C It can be noticed that, once deprived of its first term, this is an "autosequence" of the second kind, whose companion of the first kind is A014113. - _Jean-François Alcover_, Aug 19 2022
%H Reinhard Zumkeller, <a href="/A135440/b135440.txt">Table of n, a(n) for n = 0..1000</a>
%H OEIS Wiki, <a href="https://oeis.org/wiki/Autosequence">Autosequence</a>
%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (1,2).
%F From _R. J. Mathar_, Feb 19 2008: (Start)
%F O.g.f.: -1/(2*x-1) - 2/(1+x).
%F a(n) = 2^n - 2*(-1)^n. (End)
%F a(n) = 2*A014551(n-1), n>0. - _Paul Curtz_, Jun 01 2011
%F E.g.f.: exp(2*x) - 2*exp(-x). - _G. C. Greubel_, Oct 14 2016
%t f[n_]:=2/(n+1);x=4;Table[x=f[x];Numerator[x],{n,0,5!}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 12 2010 *)
%t LinearRecurrence[{1,2}, {-1,4}, 25] (* or *) Table[2^n - 2*(-1)^n, {n,0,25}] (* _G. C. Greubel_, Oct 14 2016 *)
%o (Haskell)
%o a135440 n = a135440_list !! n
%o a135440_list = zipWith (-) (tail a014551_list) a014551_list
%o -- _Reinhard Zumkeller_, Jan 02 2013
%K sign,easy
%O 0,2
%A _Paul Curtz_, Feb 18 2008
%E More terms from _R. J. Mathar_, Feb 19 2008
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