A130784 Period 3: repeat [1, 3, 2].

1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3, 2, 1, 3

Offset: 0

Author

Paul Curtz, Jul 15 2007

Keywords

• nonn
• easy

Comments

Continued fraction expansion of (3+sqrt(37))/7 (A176977). - Klaus Brockhaus, Apr 30 2010

Pairwise sums of A010872(n). - Wesley Ivan Hurt, Jul 08 2014

Decimal expansion of 44/333. - David A. Corneth, Jul 02 2016

Links

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

Crossrefs

Cf. A010872, A080425, A176977.

Programs

Magma

[(n mod 3) + ((n+1) mod 3) : n in [0..100]]; // Wesley Ivan Hurt, Jul 08 2014

Maple

A130784:=n->4-n+3*floor((n-1)/3); seq(A130784(n), n=0..100); # Wesley Ivan Hurt, Nov 30 2013

Mathematica

PadRight[{}, 111, {1,3,2}] (* Harvey P. Dale, Apr 20 2012 *)
CoefficientList[Series[(1 + 3 x + 2 x^2)/(1 - x^3), {x, 0, 120}], x] (* Michael De Vlieger, Jul 02 2016 *)

PARI

a(n)=[1,3,2][n%3+1] \\ Charles R Greathouse IV, Jun 02 2011

Formula

a(n) = 4 - n + 3*floor((n-1)/3). - Wesley Ivan Hurt, Nov 30 2013

a(n) = A080425(n) + 1. - Wesley Ivan Hurt, Jul 08 2014

a(n) = 3 - ((n+5) mod 3) = 1 + (-n mod 3). - Wesley Ivan Hurt, Aug 29 2014

From Robert Israel, Aug 29 2014: (Start)

a(n) = 3*a(n-1)^2/2 - 13*a(n-1)/2 + 8.

O.g.f.: (1+z)*(1+2*z)/(1-z^3).

E.g.f.: 2*exp(z) - 2/sqrt(3)*exp(-z/2)*cos(sqrt(3)*z/2+Pi/6). (End)

a(n) = a(n-3) for n>2. - Wesley Ivan Hurt, Jul 02 2016