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A117373 Expansion of (1-3x)/(1-x+x^2). 12
1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1, -2, -3, -1, 2, 3, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums of number triangle A117372.

Periodic sequence with period {1, -2, -3, -1, 2, 3}. [Philippe Deléham, Nov 03 2008]

LINKS

Table of n, a(n) for n=0..54.

Tanya Khovanova, Recursive Sequences

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

FORMULA

a(n) = Sum_{k=0..n} (-1)^(n-k)*(C(k,n-k)+3*C(k, n-k-1)).

a(n) = 1/6*{2*[n mod 6]-[(n+1) mod 6]-3*[(n+2) mod 6]-2*[(n+3) mod 6]+[(n+4) mod 6]+3*[(n+5) mod 6]}, with n>=1. - Paolo P. Lava, Apr 27 2007

a(n) = a(n-1)-a(n-2); a(0)=1, a(1)=-2 . [Philippe Deléham, Nov 03 2008]

a(n) = A010892(n) -3*A010892(n-1). - R. J. Mathar, Sep 14 2013

a(n) = cos(n*Pi/3) - 5*sin(n*Pi/3)/sqrt(3). - Andres Cicuttin, Apr 06 2016

MATHEMATICA

CoefficientList[Series[(1 - 3 x)/(1 - x + x^2), {x, 0, 200}], x] (* Vladimir Joseph Stephan Orlovsky, Jun 11 2011 *)

PROG

(PARI) Vec((1-3*x)/(1-x+x^2) + O(x^90)) \\ Michel Marcus, Apr 06 2016

CROSSREFS

Sequence in context: A073645 A179542 A082846 * A132677 A010882 A106590

Adjacent sequences:  A117370 A117371 A117372 * A117374 A117375 A117376

KEYWORD

easy,sign

AUTHOR

Paul Barry, Mar 10 2006

STATUS

approved

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Last modified August 23 22:23 EDT 2017. Contains 291021 sequences.