login
A238470
Period 7: repeat [0, 0, 1, 0, 0, -1, 0].
5
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.
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
KEYWORD
sign,easy
AUTHOR
Wolfdieter Lang, Feb 27 2014
STATUS
approved