A234046 Period 7: repeat [0, 1, -1, 0, 0, -1, 1].

0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1, 0, 1, -1, 0, 0, -1, 1

Offset

0

Comments

This is the sequence called c(n) in A234044 used in a formula for 2*exp(2*Pi*n*I/7) together with five other sequences: a(n) = A234044(n), b(n) = A234045(n), A(n) = A238468(n), B(n) = A238469(n) and C(n) = A238470(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*(1 - x - x^4 + x^5)/(1 - x^7).

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

From Wesley Ivan Hurt, Jul 19 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(n/7) + 2*floor((1+n)/7) - floor((2+n)/7) + floor((4+n)/7) - 2*floor((5+n)/7) + floor((6+n)/7). (End)

Maple

seq(op([0, 1, -1, 0, 0, -1, 1]), n=0..20); # Wesley Ivan Hurt, Jul 19 2016

Mathematica

PadRight[{}, 100, {0, 1, -1, 0, 0, -1, 1}] (* Wesley Ivan Hurt, Jul 19 2016 *)

Prog

(Magma) &cat [[0, 1, -1, 0, 0, -1, 1]^^20]; // Wesley Ivan Hurt, Jul 19 2016

Crossrefs

Cf. A234044, A234045, A238468, A238469, A238470.

Sequence in context: A269927 A246146 A191162 * A285565 A188076 A189011

Adjacent sequences: A234043 A234044 A234045 * A234047 A234048 A234049

Keyword

sign,easy

Author

Wolfdieter Lang, Feb 27 2014

Status

approved