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%I #24 Sep 08 2022 08:45:19
%S 1,2,4,9,20,44,96,208,448,960,2048,4352,9216,19456,40960,86016,180224,
%T 376832,786432,1638400,3407872,7077888,14680064,30408704,62914560,
%U 130023424,268435456,553648128,1140850688,2348810240
%N Second differences of A045623, prefixed by an initial 1.
%C Binomial transform of [1,1,1,2,1,3,1,...]. [From _Paul Barry_, Mar 18 2009]
%H Vincenzo Librandi, <a href="/A109975/b109975.txt">Table of n, a(n) for n = 0..1000</a>
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (4,-4).
%F G.f.: (1-2x+x^3)/(1-2x)^2. [From _Paul Barry_, Mar 18 2009]
%F a(n) = 2^(n-3)*(n+6) with n>1, a(0)=1, a(1)=2 (see the PARI code). - _Bruno Berselli_, Jun 27 2012
%F G.f.: Q(0)/(1-x), where Q(k)= 1 + (k+1)*x/(1 - x - x*(1-x)/(x + (k+1)*(1-x)/Q(k+1))); (continued fraction). - _Sergei N. Gladkovskii_, Apr 25 2013
%t CoefficientList[Series[(1-2x+x^3)/(1-2x)^2,{x,0,40}],x] (* _Vincenzo Librandi_, Jun 27 2012 *)
%o (PARI) a(n)=(n+6)<<(n-3)+(n<2) \\ _Charles R Greathouse IV_, Jun 01 2011
%o (Magma) I:=[1, 2, 4, 9]; [n le 4 select I[n] else 4*Self(n-1)-4*Self(n-2): n in [1..40]]; // _Vincenzo Librandi_, Jun 27 2012
%Y Essentially a duplicate of A034007.
%K nonn,easy
%O 0,2
%A _Paul Curtz_, Jun 07 2007
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