Search: id:A079978
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%I A079978
%S A079978 1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,
%T A079978 0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1,0,0,1
%N A079978 Number of permutations satisfying -k<=p(i)-i<=r and p(i)-i not in I, 
               i=1..n, with k=1, r=2, I={0,1}.
%C A079978 a(n)=1 if n=3k, a(n)=0 otherwise. Decimal expansion of 1/999.
%D A079978 D. H. Lehmer, Permutations with strongly restricted displacements. Combinatorial 
               theory and its applications, II (Proc. Colloq., Balatonfured, 1969), 
               pp. 755-770. North-Holland, Amsterdam, 1970.
%H A079978 <a href="Sindx_Ch.html#char_fns">Index entries for characteristic functions</
               a>
%F A079978 Recurrence: a(n) = a(n-3). G.f.: -1/(x^3-1)
%F A079978 a(n)=(1+e^(i*pi*A002487(n)))/2, i=sqrt(-1); - Paul Barry (pbarry(AT)wit.ie), 
               Jan 14 2005
%F A079978 a(n) = (2/3)*[cos(n*(2/3)* Pi)+1/2] with n>=0. This can be used to create 
               any periodic sequence of three elements x, y, z: b(n) = x*a(n) + 
               y*a(n+2) + z*a(n+1) with n>=0 - Paolo P. Lava (ppl(AT)spl.at), Aug 
               22 2006
%F A079978 Additive with a(p^e) = 1 if p = 3, 0 otherwise.
%F A079978 a(n)=-1*((n^2 mod 3)-1) - Paolo P. Lava (ppl(AT)spl.at), Oct 02 2006
%F A079978 a(n)=((n+1) mod 3) mod 2. Also: a(n)=1/2*(1+(-1)^(n+floor((n+1)/3))). 
               - Hieronymus Fischer (Hieronymus.Fischer(AT)gmx.de), May 29 2007
%o A079978 (PARI) a(n)=!(n%3) [From Jaume Oliver Lafont (joliverlafont(AT)gmail.com), 
               Mar 01 2009]
%Y A079978 Cf. A002524-A002529, A072827, A072850-A072856, A079955-A080014, A022003.
%Y A079978 Essentially the same as A022003.
%Y A079978 Partial sums are given by A002264(n+3).
%Y A079978 Sequence in context: A014099 A037011 A024692 this_sequence A164704 A068429 
               A011747
%Y A079978 Adjacent sequences: A079975 A079976 A079977 this_sequence A079979 A079980 
               A079981
%K A079978 nonn
%O A079978 0,1
%A A079978 Vladimir Baltic (baltic(AT)matf.bg.ac.yu), Feb 17 2003

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