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A108784
Difference between A107757 and A107755.
3
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, -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, -1, -1, 1, -1, 1, 1, -1, 1, -1, -1, 1, -1, 1, 1, -1, -1, 1, 1, -1, 1, -1, -1, 1
OFFSET
1,1
COMMENTS
Of the 255 terms less than 10^4, 128 are positive.
LINKS
FORMULA
It appears that a(n) = A076826(2n)-1. - T. D. Noe, Jun 14 2007
a(n) = A107757(n) - A107755(n).
MAPLE
Maple code from R. J. Mathar, Feb 25 2008:
A000108 := proc(n) option remember ; binomial(2*n, n)/(n+1) ; end:
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:
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:
A108784 := proc(n) A107757(n)-A107755(n) ; end: seq(A108784(n), n=1..120) ;
MATHEMATICA
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
CROSSREFS
KEYWORD
sign
AUTHOR
Robert G. Wilson v, Jun 14 2005
EXTENSIONS
Corrected by T. D. Noe, Jun 14 2007
STATUS
approved