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A131729
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Period 4: repeat 0, 1, -1, 1 .
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1
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0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1, -1, 1, 0, 1
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OFFSET
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0,1
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LINKS
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Table of n, a(n) for n=0..113.
M. Somos, Rational Function Multiplicative Coefficients
Index to sequences with linear recurrences with constant coefficients, signature (0,0,0,1)
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FORMULA
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Expansion of x * (1 - x) * (1 - x^6) / ((1 - x^2) * (1 - x^3) * (1 - x^4)) = (x - x^2 + x^3) / (1 - x^4) in powers of x. - Michael Somos, Apr 10 2011
Euler transform of length 6 sequence [ -1, 1, 1, 1, 0, -1]. - Michael Somos, Apr 10 2011
Moebius transform is length 4 sequence [ 1, -2, 0, 1]. - Michael Somos, Apr 10 2011
a(n) is multiplicative with a(2) = -1, a(2^e) = 0 if e>1, a(p^e) = 1 if p>2. - Michael Somos, Apr 10 2011
E.g.f.: sinh(x) + (cos(x) - cosh(x)) / 2. a(n) = a(-n) = a(n+4). a(2*n + 1) = 0. a(4*n + 2) = -1. a(4*n) = 0. - Michael Somos, Apr 10 2011
G.f. A081360 = Product_{k>0} (1 - x^k)^a(k). - Michael Somos, Feb 06 2012
a(n)=(1/24)*{7*(n mod 4)-11*[(n+1) mod 4]+13*[(n+2) mod 4]-5*[(n+3) mod 4]}, with n>=0 - Paolo P. Lava, Oct 02 2007
G.f.: -x*(1-x+x^2)/ ((x-1)*(x+1)*(x^2+1)). - R. J. Mathar, Nov 15 2007
a(n) = 1/4+(1/2)*cos(1/2*Pi*n)+3/4*(-1)^(1+n). - R. J. Mathar, Nov 15 2007
a(n)=1/4+(1/4)*I^n-(3/4)*(-1)^n+(1/4)*(-I)^n, with n>=0 and I=sqrt(-1) - Paolo P. Lava, Jul 17 2008
Dirichlet g.f. (1-2^(-s))^2*zeta(s). - R. J. Mathar, Apr 14 2011
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EXAMPLE
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x - x^2 + x^3 + x^5 - x^6 + x^7 + x^9 - x^10 + x^11 + x^13 - x^14 + x^15 + ...
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PROG
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(PARI) a(n)=!(n%4)-(-1)^n [From Jaume Oliver Lafont, Aug 28 2009]
(PARI) {a(n) = [ 0, 1, -1, 1][n%4 + 1]} /* Michael Somos, Apr 10 2011 */
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CROSSREFS
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Cf. A081360.
Sequence in context: A166486 A046978 A075553 * A144609 A115517 A022930
Adjacent sequences: A131726 A131727 A131728 * A131730 A131731 A131732
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KEYWORD
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sign,mult,easy
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AUTHOR
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Paul Curtz, Sep 17 2007
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STATUS
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approved
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