A238470 Period 7: repeat [0, 0, 1, 0, 0, -1, 0].

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

Offset

0

Comments

This sequence is called C(n) in a comment on A234044, where it appears, together with five others called a,b,c, and A, B, in a formula for 2*exp(2*Pi*n*I/7). See A234044 for details and the 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^3)/(1 - x^7).

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

From Wesley Ivan Hurt, Jul 18 2016: (Start)

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

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

Maple

seq(op([0, 0, 1, 0, 0, -1, 0]), n=0..20); # Wesley Ivan Hurt, Jul 18 2016

Mathematica

PadRight[{}, 100, {0, 0, 1, 0, 0, -1, 0}] (* Wesley Ivan Hurt, Jul 18 2016 *)

Prog

(PARI) a(n)=[0, 0, 1, 0, 0, -1, 0][n%7+1] \\ Charles R Greathouse IV, Jul 13 2016
(Magma) &cat [[0, 0, 1, 0, 0, -1, 0]^^20]; // Wesley Ivan Hurt, Jul 18 2016

Crossrefs

Cf. A234044, A234045, A234046, A238468, A238469.

Sequence in context: A099395 A182581 A288203 * A286748 A289001 A171588

Adjacent sequences: A238467 A238468 A238469 * A238471 A238472 A238473

Keyword

sign,easy

Author

Wolfdieter Lang, Feb 27 2014

Status

approved