Search: id:A100051
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%I A100051
%S A100051 1,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,
%T A100051 1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,1,1,2,
%U A100051 1,1,2,1,1
%V A100051 1,1,-1,-2,-1,1,2,1,-1,-2,-1,1,2,1,-1,-2,-1,1,2,1,-1,-2,-1,1,2,1,-1,-2,
               -1,1,2,1,-1,-2,
%W A100051 -1,1,2,1,-1,-2,-1,1,2,1,-1,-2,-1,1,2,1,-1,-2,-1,1,2,1,-1,-2,-1,1,2,1,
               -1,-2,-1,1,2,1,
%X A100051 -1,-2,-1,1,2,1,-1
%N A100051 A Chebyshev transform of 1,1,1,...
%C A100051 A Chebyshev transform of 1/(1-x): if A(x) is the g.f. of a sequence, 
               map it to ((1-x^2)/(1+x^2))A(x/(1+x^2)).
%C A100051 Transform of 1/(1+x) under the mapping g(x)->((1+x)/(1-x))g(x/(1-x)^2). 
               - Paul Barry (pbarry(AT)wit.ie), Dec 01 2004
%C A100051 Multiplicative with a(p^e) = -1 if p = 2; -2 if p = 3; 1 otherwise. David 
               W. Wilson (davidwwilson(AT)comcast.net) Jun 10, 2005.
%F A100051 G.f.: (1-x^2)/(1-x+x^2); a(n)=a(n-1)-a(n-2), n>2; a(n)=n*sum{k=0..floor(n/
               2), (-1)^k*binomial(n-k, k)/(n-k)}.
%F A100051 a(n)=sum{k=0..n, binomial(n+k, 2k)(2n/(n+k))(-1)^k}, n>1 - Paul Barry 
               (pbarry(AT)wit.ie), Dec 01 2004
%F A100051 Moebius transform is length 6 sequence [ 1, -2, -3, 0, 0, 6].
%F A100051 Euler transform of length 6 sequence [ 1, -2, -1, 0, 0, 1].
%F A100051 a(n)=A087204(n), n>0. [From R. J. Mathar (mathar(AT)strw.leidenuniv.nl), 
               Sep 02 2008]
%o A100051 (PARI) {a(n)=if(n==0, 1, [2, 1, -1, -2, -1, 1][n%6+1])}
%Y A100051 Cf. A099837, A099443, A011655, A100047, A100048, A100050.
%Y A100051 Row sums of array A127677.
%Y A100051 Sequence in context: A057559 A016010 A099837 this_sequence A122876 A100063 
               A132419
%Y A100051 Adjacent sequences: A100048 A100049 A100050 this_sequence A100052 A100053 
               A100054
%K A100051 easy,sign,mult
%O A100051 0,4
%A A100051 Paul Barry (pbarry(AT)wit.ie), Oct 31 2004

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