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%I #23 Sep 08 2022 08:45:11
%S 1,2,4,7,13,24,46,89,175,346,688,1371,2737,5468,10930,21853,43699,
%T 87390,174772,349535,699061,1398112,2796214,5592417,11184823,22369634,
%U 44739256,89478499,178956985,357913956,715827898,1431655781,2863311547
%N Partial sums of A005578.
%C With [0,0,0] prepended to it, this is an autosequence of the first kind. - _Jean-François Alcover_, Oct 21 2019
%H Vincenzo Librandi, <a href="/A086445/b086445.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_04">Index entries for linear recurrences with constant coefficients</a>, signature (3,-1,-3,2).
%F G.f.: (1-x-x^2)/((1+x)(1-x)^2(1-2x)).
%F a(n) = 2*2^n/3+(-1)^n/12+n/2+1/4.
%F a(n) = A000975(n) + A008619(n).
%F a(0) = 1, a(n) = floor(2*a(n-1) - n/2 + 1) for n>0. - _Gerald McGarvey_, Aug 31 2004
%F a(n+1) - 2*a(n) = -floor(n/2) = -A004526(n). - _Jean-François Alcover_, Oct 21 2019 [noticed by _Paul Curtz_ in a private e-mail]
%p A086445:=n->2*2^n/3+(-1)^n/12+n/2+1/4: seq(A086445(n), n=0..40); # _Wesley Ivan Hurt_, Apr 24 2017
%t CoefficientList[Series[(1-x-x^2)/((1+x)(1-x)^2(1-2x)),{x,0,40}],x] (* _Vincenzo Librandi_, Apr 05 2012 *)
%t LinearRecurrence[{3,-1,-3,2},{1,2,4,7},40] (* _Harvey P. Dale_, May 28 2015 *)
%o (Magma) [2*2^n/3+(-1)^n/12+n/2+1/4: n in [0..40]]; // _Vincenzo Librandi_, Apr 05 2012
%Y Cf. A000975, A004526, A005578, A008619.
%K nonn,easy
%O 0,2
%A _Paul Barry_, Jul 20 2003