OFFSET
0,1
COMMENTS
This sequence is the Euler transformation of A185017. - Jason Kimberley, Oct 14 2011
LINKS
FORMULA
a(n) = 0^(n mod 7).
a(0)=1, a(n)=0 for 1<=n<7, a(n+7)=a(n).
a(n) = 1 - (n^6 mod 7). - Paolo P. Lava, Oct 02 2006
a(n) = floor(n/7)-floor((n-1)/7). - Tani Akinari, Oct 26 2012
a(n) = C(n-1,6) mod 7. - Wesley Ivan Hurt, Oct 07 2014
From Wesley Ivan Hurt, Jul 11 2016: (Start)
G.f.: 1/(1-x^7).
a(n) = a(n-7) for n>6.
a(n) = (gcd(n,7) - 1)/6. (End)
EXAMPLE
a(14) = a(2*7) = 1; a(41) = a(5*7+6) = 0.
MAPLE
MATHEMATICA
Table[Mod[Binomial[n - 1, 6], 7], {n, 0, 100}] (* Wesley Ivan Hurt, Oct 07 2014 *)
Table[Boole[Divisible[n, 7]], {n, 0, 100}] (* Amiram Eldar, Oct 31 2023 *)
PROG
(Haskell)
a082784 = a000007 . (`mod` 7)
a082784_list = cycle [1, 0, 0, 0, 0, 0, 0]
-- Reinhard Zumkeller, Oct 27 2012
(PARI) a(n)=!(n%7) \\ Charles R Greathouse IV, Dec 03 2012
(Magma) [Binomial(n-1, 6) mod 7 : n in [0..100]]; // Wesley Ivan Hurt, Oct 07 2014
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, May 22 2003
EXTENSIONS
Wrong formula and keyword mult removed by Amiram Eldar, Oct 31 2023
STATUS
approved