A131734 Hexaperiodic [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, -1, 0, 1, 0, 1, 0

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

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 *)
PadRight[{}, 120, {0, 1, 0, 1, 0, -1}] (* Harvey P. Dale, Jun 09 2024 *)

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: A000035 A188510 A091337 * A134452 A327515 A327532

Adjacent sequences: A131731 A131732 A131733 * A131735 A131736 A131737

Keyword

sign,easy

Author

Paul Curtz, Sep 19 2007

Status

approved