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%I #56 Jul 04 2023 09:50:17
%S 2,0,3,1,4,2,5,3,6,4,7,5,8,6,9,7,10,8,11,9,12,10,13,11,14,12,15,13,16,
%T 14,17,15,18,16,19,17,20,18,21,19,22,20,23,21,24,22,25,23,26,24,27,25,
%U 28,26,29,27,30,28,31,29,32,30,33,31,34,32,35,33,36,34,37,35,38,36,39
%N Follow n+2 by n. Also solution of a(n+2)=a(n)+1, a(0)=2, a(1)=0.
%H Stefano Spezia, <a href="/A084964/b084964.txt">Table of n, a(n) for n = 0..10000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (1,1,-1).
%H <a href="/index/Tu#2wis">Index entries for two-way infinite sequences</a>
%F G.f.: (2-2x+x^2)/((1-x)(1-x^2)).
%F a(2n+1)=n. a(2n)=n+2. a(n+2)=a(n)+1. a(n)=-a(-3-n).
%F a(n) = floor(n/2) + 1 + (-1)^n. - _Reinhard Zumkeller_, Aug 27 2005
%F A112032(n)=2^a(n); A112033(n)=3*2^a(n); a(n)=A109613(n+2)-A052938(n). - _Reinhard Zumkeller_, Aug 27 2005
%F a(n) = n + 1 - a(n-1) (with a(0)=2). - _Vincenzo Librandi_, Aug 08 2010
%F a(n) = floor(n/2)*3 - floor((n-1)/2)*2. - _Ross La Haye_, Mar 27 2013
%F a(n) = 3*n - 3 - 5*floor((n-1)/2). - _Wesley Ivan Hurt_, Nov 08 2013
%F a(n) = (3 + 5*(-1)^n + 2*n)/4. - _Wolfgang Hintze_, Dec 13 2014
%F E.g.f.: ((4 + x)*cosh(x) - (1 - x)*sinh(x))/2. - _Stefano Spezia_, Jul 01 2023
%p A084964:=n->floor(n/2)+1+(-1)^n; seq(A084964(k), k=0..100); # _Wesley Ivan Hurt_, Nov 08 2013
%t lst={}; a=1; Do[a=n-a; AppendTo[lst, a], {n, 0, 100}]; lst (* _Vladimir Joseph Stephan Orlovsky_, Dec 14 2008 *)
%t Table[{n,n-2},{n,2,40}]//Flatten (* or *) LinearRecurrence[{1,1,-1},{2,0,3},80] (* _Harvey P. Dale_, Sep 12 2021 *)
%o (PARI) a(n)=n\2-2*(n%2)+2
%o (Magma) &cat[ [n+2, n]: n in [0..37] ]; [_Klaus Brockhaus_, Nov 23 2009]
%o (Haskell)
%o import Data.List (transpose)
%o a084964 n = a084964_list !! n
%o a084964_list = concat $ transpose [[2..], [0..]]
%o -- _Reinhard Zumkeller_, Apr 06 2015
%Y Cf. A030451, A097065, A152832.
%Y Cf. A217764(1,n) = a(n+2).
%K nonn,easy
%O 0,1
%A _Michael Somos_, Jun 15 2003
%E First part of definition adjusted to match offset by _Klaus Brockhaus_, Nov 23 2009
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