A232991 Period 6: repeat [1, 0, 0, 0, 1, 0].

1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1, 0, 1, 0, 0, 0, 1

Offset

0,1

References

Andrews, George E., q-series: their development and application in analysis, number theory, combinatorics, physics, and computer algebra. CBMS Regional Conference Series in Mathematics, 66. Published for the Conference Board of the Mathematical Sciences, Washington, DC; by the American Mathematical Society, Providence, RI, 1986. xii+130 pp. ISBN: 0-8218-0716-1 MR0858826 (88b:11063). See p. 105.

Links

Table of n, a(n) for n=0..106.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

Formula

a(n) = ceiling((n + 4)/6) - floor((n + 4)/6) - (n mod 2). - Wesley Ivan Hurt, Mar 13 2014

a(n) = cos(Pi*n/2)/3*(cos(Pi*n/6) + 2*cos(Pi*n/2) + sqrt(3)*sin(Pi*n/6)). - Vaclav Kotesovec, Mar 23 2014

G.f.: (1 + x^4)/(1 - x^6). - Bruno Berselli, Feb 18 2015

a(n) = if gcd(n+1, 6) > 1 then 0, otherwise 1. - Reinhard Zumkeller, Apr 06 2015

a(n) = a(n-6) for n > 5. - Wesley Ivan Hurt, Jun 20 2016

E.g.f.: (2*cosh(x) - sqrt(3)*sin(sqrt(3)*x/2)*sinh(x/2) + cos(sqrt(3)*x/2)*cosh(x/2))/3. - Ilya Gutkovskiy, Jun 21 2016

a(n) = gcd(gcd(floor((n+2)/3), 2), n) - 1. - Lechoslaw Ratajczak, Jul 30 2021

a(n) = sign((n+1) mod ((5+(-1)^n)/2)). - Wesley Ivan Hurt, Feb 04 2022

Maple

A232991:=n->ceil((n+4)/6) - floor((n+4)/6) - (n mod 2): seq(A232991(n), n=0..100); # Wesley Ivan Hurt, Mar 13 2014

Mathematica

Table[Ceiling[(n + 4)/6] - Floor[(n + 4)/6] - Mod[n, 2], {n, 0, 100}] (* Wesley Ivan Hurt, Mar 13 2014 *)
Table[Cos[Pi*n/2]/3 * (Cos[Pi*n/6] + 2*Cos[Pi*n/2] + Sqrt[3]*Sin[Pi*n/6]), {n, 0, 100}] (* Vaclav Kotesovec, Mar 23 2014 *)

Prog

(Magma) /* By definition: */ &cat [[1, 0, 0, 0, 1, 0]: n in [0..20]]; // Bruno Berselli, Feb 18 2015
(Magma) [(((n+3) mod 6) mod 5) mod 2: n in [0..100]]; // Vincenzo Librandi, Feb 18 2015
(Haskell)
a232991 = (0 ^) . subtract 1 . gcd 6 . (+ 1)
a232991_list = cycle [1, 0, 0, 0, 1, 0]
-- Reinhard Zumkeller, Apr 06 2015
(PARI) a(n)=(n+9)\6 - (n+4)\6 - n%2 \\ Charles R Greathouse IV, Jul 17 2016
(Python)
def A232991(n): return int(not (n+1) % 6 & 3 ^ 1) # Chai Wah Wu, May 25 2022

Crossrefs

Cf. A089128, A232990.

Sequence in context: A355688 A373154 A353488 * A168553 A267636 A267841

Adjacent sequences: A232988 A232989 A232990 * A232992 A232993 A232994

Keyword

nonn,easy

Author

N. J. A. Sloane, Dec 13 2013

Status

approved