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A132429 Period 4: repeat [3, 1, -1, -3]. 8
3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1, -1, -3, 3, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Differences: -2*(1, 1, 1, -3).

Nonsimple continued fraction expansion of (7+3*sqrt(5))/2 = 6.85410196624.. = 1 + A090550. - R. J. Mathar, Mar 08 2012

Pisano period lengths: 1, 1, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, ... . - R. J. Mathar, Aug 10 2012

LINKS

Table of n, a(n) for n=0..101.

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

FORMULA

a(n) = (1/2)*(-3*(n mod 4)+((n+1) mod 4)+((n+2) mod 4)+((n+3) mod 4)). - Paolo P. Lava, Nov 19 2007

G.f.: (3+4*x+3*x^2)/((1+x)*(1+x^2)). - Jaume Oliver Lafont, Aug 30 2009

a(n) = (1-I)*I^n+(-1)^n+(1+I)*(-I)^n, with I=sqrt(-1). - Paolo P. Lava, May 04 2010

a(n) = (-1)^n + 2(-1)^((2n + (-1)^n - 1)/4). - Brad Clardy, Mar 10 2013

a(n) = 3 - 2 * (n mod 4). - Joerg Arndt, Mar 10 2013

a(n) = (-1)^n + 2(-1)^floor(n/2). - Wesley Ivan Hurt, Apr 17 2014

From Wesley Ivan Hurt, Jul 10 2016: (Start)

a(n) + a(n-1) + a(n-2) + a(n-3) = 0 for n>2, a(n) = a(n-4) for n>3.

a(n) = 2*cos(n*Pi/2) + cos(n*Pi) + 2*sin(n*Pi/2) + I*sin(n*Pi). (End)

MAPLE

A132429:=n->3 - 2 * (n mod 4); seq(A132429(n), n=0..100); # Wesley Ivan Hurt, Apr 18 2014

MATHEMATICA

PadRight[{}, 104, {3, 1, -1, -3}] (* Harvey P. Dale, Nov 12 2011 *)

PROG

(PARI) a(n)=3-2*(n%4) \\ Jaume Oliver Lafont, Aug 28 2009

(Haskell)

a132429 = (3 -) . (* 2) . (`mod` 4)

a132429_list = cycle [3, 1, -1, -3]  -- Reinhard Zumkeller, Aug 15 2015

(MAGMA) &cat [[3, 1, -1, -3]^^30]; // Wesley Ivan Hurt, Jul 10 2016

CROSSREFS

Cf. A084101 (1, 3, 3, 1), A090550.

Sequence in context: A099545 A300867 A269301 * A046540 A123191 A157454

Adjacent sequences:  A132426 A132427 A132428 * A132430 A132431 A132432

KEYWORD

sign,easy

AUTHOR

Paul Curtz, Nov 13 2007

STATUS

approved

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Last modified January 21 05:39 EST 2020. Contains 331104 sequences. (Running on oeis4.)