A238469 - OEIS

A238469

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

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

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OFFSET

COMMENTS

This sequence is called B(n) in a comment on A234044 where it appears, together with five others, in a formula for 2*exp(2*Pi*n*I/7). See A234044 for details, also for the n = 4 example.

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^5)/(1 - x^7).

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

From Wesley Ivan Hurt, Jul 18 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) - floor((1+n)/7) - floor((5+n)/7) + floor((6+n)/7). (End)

MAPLE

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

MATHEMATICA