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A122876 a(0)=1, a(1)=1, a(2)=2, a(n) = a(n-1) - a(n-2) for n>2. 2
1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1, 1, 2, 1, -1, -2, -1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Essentially the same as A057079, A087204 and A100051.

LINKS

Table of n, a(n) for n=0..78.

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

FORMULA

a(n) = Sum_{k=0..floor(n/2)}(-2)^k*A055830(n-k,k).

G.f.: (1+2*x^2)/(1-x+x^2)^.

a(n) = (1/2)*[(1/2)-(1/2)*I*sqrt(3)]^(n-1)+(1/2)*[(1/2)+(1/2)*I*sqrt(3)]^(n-1)+(1/2)*I*[(1/2)-(1/2)*I *sqrt(3)]^(n-1)*sqrt(3)-(1/2)*I*[(1/2)+(1/2)*I*sqrt(3)]^(n-1)*sqrt(3)+[C(2*n,n) mod 2], with n>=0 and I=sqrt(-1). - Paolo P. Lava, Nov 19 2008

MATHEMATICA

LinearRecurrence[{1, -1}, {1, 1, 2}, 50] (* G. C. Greubel, May 03 2017; corrected by Georg Fischer, Apr 02 2019 *)

(* or *) CoefficientList[Series[(1 + 2*x^2)/(1 - x + x^2), {x, 0, 50}], x] (* G. C. Greubel, May 03 2017 *)

PROG

(PARI) x='x+O('x^50); Vec((1+2*x^2)/(1-x+x^2)) \\ G. C. Greubel, May 03 2017

CROSSREFS

Cf. A055830, A057079, A087204, A100051.

Sequence in context: A099837 A100051 A281727 * A131713 A100063 A057079

Adjacent sequences:  A122873 A122874 A122875 * A122877 A122878 A122879

KEYWORD

sign,easy

AUTHOR

Philippe Deléham, Oct 24 2006

STATUS

approved

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Last modified September 27 16:20 EDT 2020. Contains 337383 sequences. (Running on oeis4.)