Search: id:A002264
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%I A002264
%S A002264 0,0,0,1,1,1,2,2,2,3,3,3,4,4,4,5,5,5,6,6,6,7,7,7,8,8,8,9,9,9,10,10,
%T A002264 10,11,11,11,12,12,12,13,13,13,14,14,14,15,15,15,16,16,16,17,17,17,
%U A002264 18,18,18,19,19,19,20,20,20,21,21,21,22,22,22,23,23,23,24,24,24,25
%N A002264 Integers repeated 3 times.
%C A002264 Complement of A010872, since A010872(n)+3*a(n)=n. - Hieronymus Fischer 
               (Hieronymus.Fischer(AT)gmx.de), Jun 01 2007
%H A002264 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A002264 floor(n/3), n>=0.
%F A002264 a(n) = -1 + sum{k=0..n} {1/9*[ -2*(k mod 3)+[(k+1) mod 3]+4*[(k+2) mod 
               3]]} - Paolo P. Lava (ppl(AT)spl.at), Jun 20 2007
%F A002264 a(n)=(3n-3-sqrt(3)*(1-2cos(2*pi*(n-1)/3))*sin(2*pi*(n-1)/3)))/9. - Hieronymus 
               Fischer (Hieronymus.Fischer(AT)gmx.de), Sep 18 2007
%F A002264 a(n)=(n-A010872(n))/3. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               Sep 18 2007
%F A002264 Complex representation: a(n)=(3n-(1-r^n)*(1+r^n/(1-r)))/9 where r=exp(2*pi/
               3*i)=(-1+sqrt(3)*i)/2 and i=sqrt(-1). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               Sep 18 2007
%F A002264 a(n)=sum{0<=k<n, A022003(k)}. - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               Sep 18 2007
%F A002264 G.f.: g(x)=x^3/((1-x)(1-x^3)). - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), 
               Sep 18 2007
%F A002264 Also, floor((n^3-1)/3*n^2) (n>=1) will produce this sequence. Moreover, 
               floor((n^3-n^2)/(3*n^2-2*n)) (n>=1) will produce this sequence as 
               well. - Mohammad K. Azarian (azarian(AT)evansville.edu), Nov 08 2007
%F A002264 a(n)=(n-1+2sin(4(n+2)pi/3)/sqrt(3))/3 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), 
               Dec 05 2008]
%p A002264 P:=proc(n) local a,i,k; for i from 0 by 1 to n do a:=-1+sum('1/9*(-2*(k 
               mod 3)+((k+1) mod 3)+4*((k+2) mod 3))','k'=0..i); print(a); od; end: 
               P(100); - Paolo P. Lava (ppl(AT)spl.at), Jun 20 2007
%o A002264 (PARI) a(n)=n\3 [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), 
               Mar 25 2009]
%Y A002264 Cf. A008620.
%Y A002264 Cf. A004526, A002265, A002266, A010761, A010762, A110532, A110533.
%Y A002264 Partial sums: A130518. Other related sequences: A004526, A010872, A010873, 
               A010874.
%Y A002264 Sequence in context: A079001 A032615 A086161 this_sequence A008620 A104581 
               A113675
%Y A002264 Adjacent sequences: A002261 A002262 A002263 this_sequence A002265 A002266 
               A002267
%K A002264 nonn,easy
%O A002264 0,7
%A A002264 N. J. A. Sloane (njas(AT)research.att.com).
%E A002264 Clarified my formulas Mohammad K. Azarian (azarian(AT)evansville.edu), 
               Aug 01 2009

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