OFFSET
0
COMMENTS
This is one of the six sequences appearing in a formula for 2*exp(2*Pi*n*I/7). See A234044 for details. The present sequence there is called b(n). An example for n=4 is also given there.
LINKS
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 >= 7, with a(0) = a(1) = a(6) =0 and a(2) = -a(3) = -a(4) = a(5) = 1.
From Wesley Ivan Hurt, Jul 16 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((1+n)/7) + 2*floor((2+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 16 2016
MATHEMATICA
PadRight[{}, 100, {0, 0, 1, -1, -1, 1, 0}] (* Wesley Ivan Hurt, Jul 16 2016 *)
PROG
(Magma) &cat [[0, 0, 1, -1, -1, 1, 0]^^20]; // Wesley Ivan Hurt, Jul 16 2016
(PARI) a(n)=(n+2)\7*2 - (n+1)\7 - (n+4)\7*2 + (n+5)\7 \\ Charles R Greathouse IV, Jul 16 2016
CROSSREFS
KEYWORD
sign,easy
AUTHOR
Wolfdieter Lang, Feb 27 2014
STATUS
approved