%I A007494
%S A007494 0,2,3,5,6,8,9,11,12,14,15,17,18,20,21,23,24,26,27,29,30,32,33,35,36,38,
%T A007494 39,41,42,44,45,47,48,50,51,53,54,56,57,59,60,62,63,65,66,68,69,71,72,
               74,
%U A007494 75,77,78,80,81,83,84,86,87,89,90,92,93,95,96,98,99,101,102,104,105,107
%N A007494 Congruent to 0 or 2 mod 3.
%C A007494 The map n -> a(n) (where a(n) = 3n/2 if n even or (3n+1)/2 if n odd) 
               was studied by Mahler, in connection with "Z-numbers" and later by 
               Flatto. One question was whether, iterating from an initial integer, 
               one eventually encountered an iterate = 1 (mod 4). - Jeff Lagarias, 
               Sep 23, 2002.
%C A007494 Partial sums of 0,2,1,2,1,2,1,2,1.... - Paul Barry (pbarry(AT)wit.ie), 
               Aug 18 2007
%C A007494 A145389(a(n)) <> 1. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Oct 10 2008]
%D A007494 L. Flatto, Z-numbers and beta-transformations, in Symbolic dynamics and 
               its applications (New Haven, CT, 1991), 181-201, Contemp. Math., 
               135, Amer. Math. Soc., Providence, RI, 1992.
%D A007494 K. Mahler, An unsolved problem on the powers of 3/2, J. Austral. Math. 
               Soc. 8 1968 313-321.
%D A007494 Sabinin, P. and Stone, M. G. ``Transforming n-gons by Folding the Plane.'' 
               Amer. Math. Monthly 102, 620-627, 1995.
%H A007494 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=1002">
               Encyclopedia of Combinatorial Structures 1002</a>
%H A007494 Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/
               Folding.html">Link to a section of The World of Mathematics.</a>
%F A007494 a(n) = 3n/2 if n even or (3n+1)/2 if n odd.
%F A007494 If u(1)=0, u(n)=n+floor(u(n-1)/3), then a(n-1)=u(n) - Benoit Cloitre 
               (benoit7848c(AT)orange.fr), Nov 26 2002
%F A007494 G.f.: x(x+2)/(1-x)^2/(1+x). - Ralf Stephan (ralf(AT)ark.in-berlin.de), 
               Apr 13 2002
%F A007494 a(n) = 3*floor(n/2) + 2*(n mod 2) = A032766(n)+A000035(n). - Reinhard 
               Zumkeller (reinhard.zumkeller(AT)gmail.com), Apr 04 2005
%F A007494 a(n)=(6n+1)/4-(-1)^n/4; a(n)=sum{k=0..n-1, 1+(-1)^(k/2)*cos(k*pi/2)}; 
               - Paul Barry (pbarry(AT)wit.ie), Aug 18 2007
%F A007494 Except for the first term, if a(1)=2, a(2)=3; a(n)=a(n-1)+1 (n even); 
               a(n)=a(n-1)+2 (n odd) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Aug 10 2009]
%F A007494 a(n)=3*n-a(n-1)-4 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 21 2009]
%e A007494 For n=2, a(2)=3*2-0-4=2; n=3, a(3)=3*3-2-4=3; n=4, a(4)=3*4-3-4=5 [From 
               Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 21 2009]
%p A007494 a[0]:=0:a[1]:=2:for n from 2 to 100 do a[n]:=a[n-2]+3 od: seq(a[n], n=0..71); 
               - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 16 2008
%p A007494 with (combinat):seq(count(Partition((3*n+1)), size=2), n=0..71); - Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Mar 28 2008
%p A007494 seq(add(irem(2^k,3),k=1..n),n=0..71); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 20 2008
%t A007494 sn=sd=s=0;lst={};Do[a=n^2+n;b=n^2-n;c=a/b;sd+=Denominator[c];sn+=Numerator[c];
               AppendTo[lst,s=sn-sd],{n,2,5!}];lst [From Vladimir Orlovsky (4vladimir(AT)gmail.com), 
               Oct 20 2009]
%Y A007494 Cf. A063574.
%Y A007494 Cf. A001651, A032766, A035361, A132462.
%Y A007494 Complement of A016777. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Oct 10 2008]
%Y A007494 Sequence in context: A061054 A061723 A045506 this_sequence A052490 A117672 
               A139364
%Y A007494 Adjacent sequences: A007491 A007492 A007493 this_sequence A007495 A007496 
               A007497
%K A007494 nonn,easy,new
%O A007494 0,2
%A A007494 Christopher Lam Cham Kee (Topher(AT)CyberDude.Com)