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A234045 Period 7: repeat [0, 0, 1, -1, -1, 1, 0]. 5
0, 0, 1, -1, -1, 1, 0, 0, 0, 1, -1, -1, 1, 0, 0, 0, 1, -1, -1, 1, 0, 0, 0, 1, -1, -1, 1, 0, 0, 0, 1, -1, -1, 1, 0, 0, 0, 1, -1, -1, 1, 0, 0, 0, 1, -1, -1, 1, 0, 0, 0, 1, -1, -1, 1, 0, 0, 0, 1, -1, -1, 1, 0, 0, 0, 1, -1, -1, 1, 0, 0, 0, 1, -1, -1, 1, 0, 0, 0, 1, -1, -1, 1, 0, 0, 0, 1, -1, -1, 1, 0 (list; graph; refs; listen; history; text; internal format)
OFFSET

0

COMMENTS

This is one of the six sequences appearing in a formula for 2*exp(2*Pi*n*I/7). See A234044 for details. The present sequence there is called b(n). An example for n=4 is also given there.

LINKS

Table of n, a(n) for n=0..90.

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

FORMULA

G.f.: x^2*(1 - x - x^2 + x^3)/(1 - x^7).

a(n+7) = a(n), n >= 7, with a(0) = a(1) = a(6) =0 and a(2) = -a(3) = -a(4) = a(5) = 1.

From Wesley Ivan Hurt, Jul 16 2016: (Start)

a(n) + a(n-1) + a(n-2) + a(n-3) + a(n-4) + a(n-5) + a(n-6) = 0, for n>5.

a(n) = - floor((1+n)/7) + 2*floor((2+n)/7) - 2*floor((4+n)/7) + floor((5+n)/7). (End)

MAPLE

seq(op([0, 0, 1, -1, -1, 1, 0]), n=0..20); # Wesley Ivan Hurt, Jul 16 2016

MATHEMATICA

PadRight[{}, 100, {0, 0, 1, -1, -1, 1, 0}] (* Wesley Ivan Hurt, Jul 16 2016 *)

PROG

(MAGMA) &cat [[0, 0, 1, -1, -1, 1, 0]^^20]; // Wesley Ivan Hurt, Jul 16 2016

(PARI) a(n)=(n+2)\7*2 - (n+1)\7 - (n+4)\7*2 + (n+5)\7 \\ Charles R Greathouse IV, Jul 16 2016

CROSSREFS

Cf. A234044, A234046, A238468, A238469, A238470.

Sequence in context: A072126 A287125 A339051 * A238468 A111113 A095190

Adjacent sequences:  A234042 A234043 A234044 * A234046 A234047 A234048

KEYWORD

sign,easy

AUTHOR

Wolfdieter Lang, Feb 27 2014

STATUS

approved

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Last modified May 6 01:50 EDT 2021. Contains 343579 sequences. (Running on oeis4.)