%I A032766
%S A032766 0,1,3,4,6,7,9,10,12,13,15,16,18,19,21,22,24,25,27,28,30,31,33,34,36,
%T A032766 37,39,40,42,43,45,46,48,49,51,52,54,55,57,58,60,61,63,64,66,67,69,70,
%U A032766 72,73,75,76,78,79,81,82,84,85,87,88,90,91,93,94,96,97,99,100,102,103
%N A032766 Numbers that are congruent to 0 or 1 mod 3.
%C A032766 Also (omitting initial 0) number of 1's in n-th row of triangle in A071039. 
               - Hans Havermann (pxp(AT)rogers.com), May 26 2002
%C A032766 Binomial transform is A053220. - Michael Somos, Jul 10 2003
%C A032766 Smallest number of different people in a set of n-1 photographs which 
               satisfies the following conditions: In each photograph there are 
               3 women, the woman in the middle is the mother of the person on her 
               left and is a sister of the person on her right and the women in 
               the middle of the photographs are all different. - Fung Cheok Yin 
               (cheokyin_restart(AT)yahoo.com.hk), Sep 22 2006
%C A032766 A004396(a(n)) = n. [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), 
               Oct 30 2009]
%D A032766 International Mathematical Olympiad 2001, Hong Kong Preliminary Selection 
               Contest Problem #20.
%H A032766 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A032766 G.f.: (x+2*x^2)/((1-x)*(1-x^2)).
%F A032766 Formulae from Paul Barry (pbarry(AT)wit.ie), Sep 04 2003: a(n)=(6*n-1+(-1)^n)/
               4; a(n)=floor((3n+2)/2)-1 = A001651(n)-1; a(n)=sqrt(2)*sqrt((6n-1)(-1)^n+18n^2-6n+1)/
               4; a(n)=sum{k=0..n, 3/2-2*0^n+(-1)^n/2}.
%F A032766 a(n) = 3*floor(n/2) + n mod 2 = A007494(n)-A000035(n). - Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Apr 04 2005
%F A032766 a(n)=2*A004526(n)+A004526(n+1). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Aug 07 2006
%F A032766 a(n) = 1 + ceiling(1.5*(n-1)) - Fung Cheok Yin (cheokyin_restart(AT)yahoo.com.hk), 
               Sep 22 2006
%F A032766 Row sums of triangle A133083. - Gary W. Adamson (qntmpkt(AT)yahoo.com), 
               Sep 08 2007
%F A032766 a(n) = (cos(Pi n) - 1)/4 + 1.5n [From Bart Snapp (snapp(AT)coastal.edu), 
               Sep 18 2008]
%F A032766 a(n)=3*n-a(n-1)-5 (with a(1)=0) [From Vincenzo Librandi (vincenzo.librandi(AT)tin.it), 
               Nov 21 2009]
%e A032766 For n=2, a(2)=3*2-0-5=1; n=3, a(3)=3*3-1-5=3; n=4, a(4)=3*4-3-5=4 [From 
               Vincenzo Librandi (vincenzo.librandi(AT)tin.it), Nov 21 2009]
%p A032766 a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=a[n-2]+3 od: seq(a[n], n=0..69); 
               - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 16 2008
%p A032766 seq(add(irem(2^k,3),k=2..n),n=1..70); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Apr 20 2008
%p A032766 Digits := 100: t := evalf(1+cos(Pi/3)): A:= n->floor(t*n): seq(floor((t*n)),
               n=0..69);# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 
               27 2009]
%p A032766 a[0]:=0:a[1]:=1:for n from 2 to 100 do a[n]:=a[n-2]+3 od: seq(a[n], n=0..69); 
               - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 16 2008
%o A032766 (PARI) a(n)=n+n\2.
%Y A032766 For n>0, a(n)=T(n, 2), array T as in A049615. Column 1 of A026374.
%Y A032766 Partial sums are A006578. Partial sums of A000034. Cf. A084056, A047270.
%Y A032766 Cf. A001651, A007494, A035360, A132463.
%Y A032766 Cf. A133083.
%Y A032766 Sequence in context: A026322 A049624 A084056 this_sequence A064717 A109231 
               A140098
%Y A032766 Adjacent sequences: A032763 A032764 A032765 this_sequence A032767 A032768 
               A032769
%K A032766 nonn,easy,nice,new
%O A032766 0,3
%A A032766 Patrick De Geest (pdg(AT)worldofnumbers.com), May 15, 1998.
%E A032766 Better description from N. J. A. Sloane (njas(AT)research.att.com) 8/
               98.