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A108784 Difference between A107757 and A107755.

%I A108784 #9 Aug 08 2015 21:57:04
%S A108784 1,1,-1,1,-1,-1,1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,-1,1,1,-1,1,
%T A108784 -1,-1,1,1,-1,-1,1,-1,1,1,-1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,
%U A108784 1,-1,-1,1,-1,1,1,-1,1,-1,-1,1,-1,1,1,-1,-1,1,1,-1,1,-1,-1,1
%N A108784 Difference between A107757 and A107755.
%C A108784 Of the 255 terms less than 10^4, 128 are positive.
%H A108784 R. J. Mathar, <a href="/A108784/b108784.txt">Table of n, a(n) for n = 1..120</a>
%F A108784 It appears that a(n) = A076826(2n)-1. - _T. D. Noe_, Jun 14 2007
%F A108784 a(n) = A107757(n) - A107755(n).
%p A108784 Maple code from _R. J. Mathar_, Feb 25 2008:
%p A108784 A000108 := proc(n) option remember ; binomial(2*n,n)/(n+1) ; end:
%p A108784 A107757 := proc(n) option remember ; local a; if n = 1 then 3; else for a from A107757(n-1)+1 do if add(A000108(k),k=1..a) mod 3 = 2 then RETURN(a) ; fi ; od: fi ; end:
%p A108784 A107755 := proc(n) option remember ; local a; if n = 1 then 2; else for a from A107755(n-1)+1 do if add(A000108(k),k=1..a) mod 3 = 0 then RETURN(a) ; fi ; od: fi ; end:
%p A108784 A108784 := proc(n) A107757(n)-A107755(n) ; end: seq(A108784(n),n=1..120) ;
%t A108784 s0 = s2 = {}; s = 0; Do[s = Mod[s + (2 n)!/n!/(n + 1)!, 3]; Switch[ Mod[s, 3], 0, AppendTo[s0, n], 2, AppendTo[s2, n]], {n, 10^4}]; s2 - s0
%Y A108784 Cf. A107755, A107756, A107757.
%K A108784 sign
%O A108784 1,1
%A A108784 _Robert G. Wilson v_, Jun 14 2005
%E A108784 Corrected by _T. D. Noe_, Jun 14 2007