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%I #34 Sep 08 2022 08:45:10
%S 1,7,9,23,41,87,169,343,681,1367,2729,5463,10921,21847,43689,87383,
%T 174761,349527,699049,1398103,2796201,5592407,11184809,22369623,
%U 44739241,89478487,178956969,357913943,715827881,1431655767,2863311529
%N a(n) = (8*2^n-5*(-1)^n)/3.
%C Binomial transform of A083581.
%H Vincenzo Librandi, <a href="/A083582/b083582.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) = (8*2^n-5(-1)^n)/3.
%F G.f.: (1+6*x)/((1-2*x)*(1+x)).
%F E.g.f.: (8*exp(2*x)-5*exp(-x))/3.
%F a(n) = 6*A001045(n) + A001045(n+1). - _Creighton Dement_, Mar 25 2005
%F a(n) = 2^(n+2)th coefficient of - eta(z)^3 eta(z^5) eta(z^10)^2 /eta(z^2)^2. - Kok Seng Chua (chuaks(AT)ihpc.a-star.edu.sg), Aug 30 2005
%F a(n) = a(n-1)+2*a(n-2). a(n)+a(n+1) = 8*A000079 = a(n+2)-a(n). - _Paul Curtz_, Jul 27 2008
%p BB := n->if n=1 then 3; > elif n=2 then 1; > else 2*BB(n-2)+BB(n-1); > fi: > L:=[]: for k from 2 to 32 do L:=[op(L),BB(k)]: od: L; # _Zerinvary Lajos_, Mar 19 2007
%t f[n_]:=2/(n+1);x=6;Table[x=f[x];Denominator[x],{n,0,5!}] (* _Vladimir Joseph Stephan Orlovsky_, Mar 12 2010 *)
%t LinearRecurrence[{1,2},{1,7},40] (* _Harvey P. Dale_, May 28 2017 *)
%o (Magma) [(8*2^n-5*(-1)^n)/3: n in [0..30]]; // _Vincenzo Librandi_, Aug 13 2011
%o (PARI) a(n)=(8*2^n-5*(-1)^n)/3 \\ _Charles R Greathouse IV_, Oct 07 2015
%Y Cf. A140966.
%K easy,nonn
%O 0,2
%A _Paul Barry_, May 01 2003
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