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A131734 Hexaperiodic [0, 1, 0, 1, 0, -1]. 1
0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0, -1, 0, 1, 0, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Table of n, a(n) for n=0..118.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

FORMULA

a(n) = (1/45)*{-7*(n mod 6)+8*[(n+1) mod 6]+8*[(n+2) mod 6]-7*[(n+3) mod 6]+8*[(n+4) mod 6]-7*[(n+5) mod 6]}. - Paolo P. Lava, Oct 02 2007

From Wesley Ivan Hurt, Apr 06 2015: (Start)

G.f.: x*(1+x^2-x^4)/(1-x^6).

Recurrence: a(n) = a(n-6).

a(n) = (1-(-1)^n)*(-1)^floor(2n/3)/2.

abs(a(n)) = A000035(n). (End)

EXAMPLE

G.f. = x + x^3 - x^5 + x^7 + x^9 - x^11 + x^13 + x^15 - x^17 + x^19 + x^21 + ...

MAPLE

A131734:=n->(1-(-1)^n)*(-1)^floor(2*n/3)/2: seq(A131734(n), n=0..100); # Wesley Ivan Hurt, Apr 06 2015

MATHEMATICA

CoefficientList[Series[x (1 + x^2 - x^4)/(1 - x^6), {x, 0, 100}], x] (* Wesley Ivan Hurt, Apr 06 2015 *)

PROG

(MAGMA) [(1-(-1)^n)*(-1)^Floor(2*n/3)/2 : n in [0..100]]; // Wesley Ivan Hurt, Apr 06 2015

(PARI) {a(n) = [ 0, 1, 0, 1, 0, -1, 0, 1][n%6 + 1]}; /* Michael Somos, Nov 11 2015 */

CROSSREFS

Cf. A000035 (absolute value).

Sequence in context: A125122 A000035 A188510 * A134452 A073445 A179081

Adjacent sequences:  A131731 A131732 A131733 * A131735 A131736 A131737

KEYWORD

sign,easy

AUTHOR

Paul Curtz, Sep 19 2007

STATUS

approved

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Last modified February 19 20:48 EST 2018. Contains 299357 sequences. (Running on oeis4.)