Search: id:A059841
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%I A059841
%S A059841 1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,
               0,1,0,1,0,1,0,
%T A059841 1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,
               0,1,0,1,0,1,0,
%U A059841 1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,
               0,1,0,1,0,1,0
%N A059841 A simple periodic sequence.
%C A059841 When viewed as an array the row sum values are 1 1 1 2 3 3 3 4 5 5 5 
               6 ... A004525
%C A059841 This is the r=0 member of the r-family of sequences S_r(n) defined in 
               A092184 where more information can be found.
%C A059841 Successive binomial transforms of this sequence : A011782, A007051, A007582, 
               A081186, A081187, A081188, A081189, A081190, A060531, A081192
%C A059841 Characteristic function of even numbers: a(A005843(n))=1, a(A005408(n))=0. 
               [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Sep 29 
               2008]
%D A059841 Paul Barry, A Catalan Transform and Related Transformations on Integer 
               Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.
%H A059841 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%H A059841 <a href="Sindx_Ch.html#char_fns">Index entries for characteristic functions</
               a>
%F A059841 G.f.: 1/(1-x^2). E.g.f.: cosh(x). a(n)=(n+1)mod 2. a(n)=1/2 + (-1)^n/
               2. - Paul Barry (pbarry(AT)wit.ie), Mar 11 2003
%F A059841 T(n, k)=([n/2]+n+k+1)mod 2, 0<=k<=n.
%F A059841 Additive with a(p^e) = 1 if p = 2, 0 otherwise.
%F A059841 a(n)= {sin[(n+1)*Pi/2]}^2 = [cos(n*Pi/2)]^2 with n>=0 - Paolo P. Lava 
               (ppl(AT)spl.at), Nov 17 2006
%F A059841 a(n)= Sum_{k, 0<=k<=n}(-1)^k*A038137(n,k) . - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 30 2006
%p A059841 with(combstruct):ZL2:=[S,{S=Set(Cycle(Z,card=2))}, unlabeled]:seq(count(ZL2,
               size=n),n=0..100); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), 
               Sep 24 2007
%t A059841 CellularAutomaton[50, {{1}, 0}, 104, {All, {0}}] // Flatten [From Zerinvary 
               Lajos (zerinvarylajos(AT)yahoo.com), Jul 08 2009]
%o A059841 (PARI) {a(n)=(n+1)%2} {T(n,k)=if(k<0|k>n,0,(n\2+n+k+1)%2)}
%Y A059841 Ones complement of A000035. Cf. A004525, A011782.
%Y A059841 Sequence in context: A101455 A056594 A091337 this_sequence A071022 A071025 
               A162549
%Y A059841 Adjacent sequences: A059838 A059839 A059840 this_sequence A059842 A059843 
               A059844
%K A059841 easy,nonn,tabl
%O A059841 0,1
%A A059841 Alford Arnold (Alford1940(AT)aol.com), Feb 25 2001

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