A131290 - OEIS

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A131290

1 followed by period 6: repeat [3, 2, 0, -1, 0, 2].

1, 3, 2, 0, -1, 0, 2, 3, 2, 0, -1, 0, 2, 3, 2, 0, -1, 0, 2, 3, 2, 0, -1, 0, 2, 3, 2, 0, -1, 0, 2, 3, 2, 0, -1, 0, 2, 3, 2, 0, -1, 0, 2, 3, 2, 0, -1, 0, 2, 3, 2, 0, -1, 0, 2, 3, 2, 0, -1, 0, 2, 3, 2, 0, -1, 0, 2, 3, 2, 0, -1, 0, 2, 3, 2, 0, -1, 0, 2, 3, 2, 0, -1, 0, 2, 3, 2, 0, -1, 0, 2, 3, 2, 0, -1, 0, 2, 3, 2, 0, -1

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..100.

Index entries for linear recurrences with constant coefficients, signature (2,-2,1).

FORMULA

G.f.: (1+x-2*x^2+x^3)/((1-x)*(1-x+x^2)). - R. J. Mathar, Feb 27 2008

If n mod 6 = 4 then a(n) = (Fibonacci(n-3)*Fibonacci(n+1)) mod 4 -2, else a(n) = (Fibonacci(n-3)*Fibonacci(n+1)) mod 4, n>0. - Gary Detlefs, Dec 12 2010

From Wesley Ivan Hurt, Jun 20 2016: (Start)

a(n) = 2*a(n-1) - 2*a(n-2) + a(n-3) for n>4.

a(0) = 1, a(n) = 1 + cos(n*Pi/3) + sqrt(3)*sin(n*Pi/3) for n>0. (End)

MAPLE

A131290 := proc(n) if n = 0 then 1; else op(((n-1)mod 6)+1, [3, 2, 0, -1, 0, 2]) ; fi ; end: seq(A131290(n), n=0..100) ; # R. J. Mathar, Feb 27 2008

MATHEMATICA

PadRight[{1}, 110, {2, 3, 2, 0, -1, 0}] (* or *) Join[{1}, LinearRecurrence[ {2, -2, 1}, {3, 2, 0}, 110]] (* Harvey P. Dale, Jun 22 2012 *)

PROG

(Magma) [1] cat &cat [[3, 2, 0, -1, 0, 2]^^30]; // Wesley Ivan Hurt, Jun 20 2016

CROSSREFS

Cf. A079757, A100219, A130869.

Sequence in context: A187145 A285700 A290693 * A138741 A116604 A303913

Adjacent sequences: A131287 A131288 A131289 * A131291 A131292 A131293

KEYWORD

sign,easy

AUTHOR

Paul Curtz, Sep 29 2007

EXTENSIONS

More terms from R. J. Mathar, Feb 27 2008

STATUS

approved