A186809 Period 6 sequence [0, 1, 2, 0, -2, -1, ...].

0, 1, 2, 0, -2, -1, 0, 1, 2, 0, -2, -1, 0, 1, 2, 0, -2, -1, 0, 1, 2, 0, -2, -1, 0, 1, 2, 0, -2, -1, 0, 1, 2, 0, -2, -1, 0, 1, 2, 0, -2, -1, 0, 1, 2, 0, -2, -1, 0, 1, 2, 0, -2, -1, 0, 1, 2, 0, -2, -1, 0, 1, 2, 0, -2, -1, 0, 1, 2, 0, -2, -1, 0, 1, 2, 0, -2, -1, 0, 1, 2, 0, -2, -1, 0, 1, 2, 0, -2, -1, 0

Offset: 0

Author

Michael Somos, Feb 26 2011

Keywords

• sign
• mult
• easy

Comments

For n > 0: a(n) = A262565(n+1) - A262565(n). - Reinhard Zumkeller, Oct 19 2015

Examples

			G.f. = x + 2*x^2 - 2*x^4 - x^5 + x^7 + 2*x^8 - 2*x^10 - x^11 + x^13 + ...
		

Links

• Michael Somos, Rational Function Multiplicative Coefficients
• Index entries for linear recurrences with constant coefficients, signature (0,-1,0,-1)

Crossrefs

Cf. A193680.

Cf. A262565.

Programs

Haskell

a186809 n = a186809_list !! (n-1)
a186809_list = cycle [0, 1, 2, 0, -2, -1]
-- Reinhard Zumkeller, Oct 19 2015

Magma

[(((n+1) mod 3)-1)*(((n+1) mod 2)+1)*(-1)^(n+1) : n in [0..100]]; // Wesley Ivan Hurt, Aug 31 2014

Maple

A186809:=n->(((n+1) mod 3)-1)*(((n+1) mod 2)+1)*(-1)^(n+1): seq(A186809(n), n=0..100); # Wesley Ivan Hurt, Aug 31 2014

Mathematica

Table[(Mod[n + 1, 3] - 1) (Mod[n + 1, 2] + 1) (-1)^(n + 1), {n, 0, 100}] (* Wesley Ivan Hurt, Aug 31 2014 *)
PadRight[{},120,{0,1,2,0,-2,-1}] (* Harvey P. Dale, Nov 18 2020 *)

PARI

{a(n) = [0, 1, 2, 0, -2, -1][n%6 + 1]};

Formula

Euler transform of length 6 sequence [2, -3, 0, 0, 0, 1].

a(n) is multiplicative with a(2^e) = -2 * (-1)^e if e>0. a(3^e) = 0^e, a(p^e) = 1 if p == 1 (mod 6), a(p^e) = (-1)^n if p == 5 (mod 6).

G.f.: x * (1 + x)^2 / (1 + x^2 + x^4). a(n+3) = a(-n) = -a(n). a(n) = n if |n| < 3.

a(n) = (mod(n+1, 3) - 1) * (mod(n+1, 2) + 1) * (-1)^(n+1). - Wesley Ivan Hurt, Aug 31 2014

|a(n)| = A193680(n). - Wesley Ivan Hurt, Aug 31 2014