Search: id:A098554
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%I A098554
%S A098554 0,1,1,2,3,1,4,1,3,2,1,1,0,1,1,2,3,1,4,1,3,2,1,1,0,1,1,2,3,1,4,1,3,2,1,
               1,
%T A098554 0,1,1,2,3,1,4,1,3,2,1,1,0,1,1,2,3,1,4,1,3,2,1,1,0,1,1,2,3,1,4,1,3,2,1,
%U A098554 1,0,1,1,2,3,1,4,1,3,2,1,1,0,1,1,2,3,1,4,1,3,2,1,1,0,1,1,2,3,1,4,1,3,2
%V A098554 0,1,-1,-2,3,1,-4,1,3,-2,-1,1,0,1,-1,-2,3,1,-4,1,3,-2,-1,1,0,1,-1,-2,3,
               1,-4,1,3,-2,-1,1,
%W A098554 0,1,-1,-2,3,1,-4,1,3,-2,-1,1,0,1,-1,-2,3,1,-4,1,3,-2,-1,1,0,1,-1,-2,3,
               1,-4,1,3,-2,-1,
%X A098554 1,0,1,-1,-2,3,1,-4,1,3,-2,-1,1,0,1,-1,-2,3,1,-4,1,3,-2,-1,1,0,1,-1,-2,
               3,1,-4,1,3,-2
%N A098554 G.f.: x*(1-x^2)/((1+x^2)*(1+x+x^2).
%D A098554 G. I. Lehrer and G. B. Segal, Homology stability for classical regular 
               semisimple varieties, Math. Zeit., 236 (2001), 251-290; see Th. 7.12.
%H A098554 <a href="Sindx_Rea.html#recLCC">Index entries for sequences related to 
               linear recurrences with constant coefficients</a>
%F A098554 Let b(n)=sum{k=0..floor(n/2), binomial(n-k, k)(0^(n-2k)-(-1)^(n-2k)}. 
               Then a(n)=b(n)-b(n-2), or a(n)=sum{j=0..n, b(n-j)(binomial(1, j/2)(-1)^(j/
               2)(1+(-1)^j)/2}. The g.f. is obtained from the g.f. x/(1+x) of 0^n-(-1)^n 
               by applying the transformation G(x)->((1-x^2)/(1+x^2))G(x/(1+x^2)). 
               - Paul Barry (pbarry(AT)wit.ie), Oct 26 2004
%Y A098554 Sequence in context: A138967 A035612 A089555 this_sequence A109201 A002946 
               A035426
%Y A098554 Adjacent sequences: A098551 A098552 A098553 this_sequence A098555 A098556 
               A098557
%K A098554 sign
%O A098554 0,4
%A A098554 N. J. A. Sloane (njas(AT)research.att.com), Oct 26 2004

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