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A105384 Expansion of x/(1 + x + x^2 + x^3 + x^4). 3
0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0, 0, 1, -1, 0, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Inverse binomial transform of A103311. A transform of the Fibonacci numbers: apply the Chebyshev transform (1/(1+x^2), x/(1+x^2)) followed by the binomial involution (1/(1-x),-x/(1-x)) followed by the inverse binomial transform (1/(1+x), x/(1+x)) (expressed as Riordan arrays) to the -F(n); equivalently, apply (1/(1+x^2),-x/(1+x^2)) to -F(n). Periodic {0,1,-1,0,0}.

Essentially the same as A010891. - R. J. Mathar, Apr 07 2008

LINKS

Table of n, a(n) for n=0..104.

Index entries for linear recurrences with constant coefficients, signature (-1,-1,-1,-1).

FORMULA

Euler transform of length 5 sequence [ -1, 0, 0, 0, 1].

G.f.: x(1-x)/(1-x^5);

a(n) = -sqrt(1/5 + 2*sqrt(5)/25)*cos(4*Pi*n/5 + Pi/10) + sqrt(5)*sin(4*Pi*n/5 + Pi/10)/5 + sqrt(1/5 - 2*sqrt(5)/25)*cos(2*Pi*n/5 + 3*Pi/10) + sqrt(5)*sin(2*Pi*n/5 + 3*Pi/10)/5.

a(n) = -(1/5)*(((n+2) mod 5) - 2*((n+3) mod 5) + ((n+4) mod 5)) with n >= 0. - Paolo P. Lava, Nov 21 2006

a(n) = A010891(n-1). - R. J. Mathar, Apr 07 2008

CROSSREFS

Sequence in context: A261185 A093692 A254114 * A288694 A292077 A327256

Adjacent sequences:  A105381 A105382 A105383 * A105385 A105386 A105387

KEYWORD

easy,sign

AUTHOR

Paul Barry, Apr 02 2005

EXTENSIONS

Corrected by N. J. A. Sloane, Nov 05 2005

STATUS

approved

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Last modified April 7 00:47 EDT 2020. Contains 333291 sequences. (Running on oeis4.)