A238468 Period 7: repeat [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, 0, 0, -1, 1, -1, 1, 0

Offset

0

Comments

This is the sequence called A(n) in a comment on A234044, which appears with five others in a formula for 2*exp(2*Pi*n*I/7). See A234044 for details and an example for n = 4.

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

From Wesley Ivan Hurt, Jul 17 2016: (Start)

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

a(n) = - floor((1+n)/7) + 2*floor((2+n)/7) - 2*floor((3+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 17 2016

Mathematica

PadRight[{}, 100, {0, 0, -1, 1, -1, 1, 0}] (* Wesley Ivan Hurt, Jul 17 2016 *)

Prog

(Magma) &cat [[0, 0, -1, 1, -1, 1, 0]^^20]; // Wesley Ivan Hurt, Jul 17 2016
(PARI) a(n)=(n+2)\7*2 - (n+3)\7*2 + (n+4)\7*2 - (n+5)\7 - (n+1)\7 \\ Charles R Greathouse IV, Jul 17 2016

Crossrefs

Cf. A234044, A234045, A234046, A238469, A238470.

Sequence in context: A287125 A339051 A234045 * A111113 A095190 A131735

Adjacent sequences: A238465 A238466 A238467 * A238469 A238470 A238471

Keyword

sign,easy

Author

Wolfdieter Lang, Feb 27 2014

Status

approved