A108784 Difference between A107757 and A107755.

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

Author

Robert G. Wilson v, Jun 14 2005

Keywords

• sign

Comments

Of the 255 terms less than 10^4, 128 are positive.

Links

• R. J. Mathar, Table of n, a(n) for n = 1..120

Crossrefs

Cf. A107755, A107756, A107757.

Programs

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

Formula

It appears that a(n) = A076826(2n)-1. - T. D. Noe, Jun 14 2007

a(n) = A107757(n) - A107755(n).

Extensions

Corrected by T. D. Noe, Jun 14 2007