A131598 Period 3: repeat [2, 5, 8].

2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8, 2, 5, 8

Offset

0,1

Comments

From Klaus Brockhaus, May 16 2010: (Start)

Continued fraction expansion of (85+sqrt(9029))/82.

Decimal expansion of 86/333. (End)

Links

Table of n, a(n) for n=0..104.

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

Formula

a(n) = 5 - 3*cos(2/3*Pi*n) - 3^(1/2)*sin(2/3*Pi*n). - R. J. Mathar, Nov 15 2007

G.f.: (2+5*x+8*x^2)/(1-x^3). - Jaume Oliver Lafont, Mar 24 2009

a(n) = a(n-3) for n>2. - Wesley Ivan Hurt, Jul 01 2016

a(n) = 3*(n mod 3) + 2, see PARI code. - Bruno Berselli, Jul 25 2018

E.g.f.: 5*exp(x) - exp(-x/2)*(3*cos(sqrt(3)*x/2) + sqrt(3)*sin(sqrt(3)*x/2)). - Stefano Spezia, Sep 11 2022

Maple

seq(op([2, 5, 8]), n=0..50); # Wesley Ivan Hurt, Jul 01 2016

Mathematica

PadRight[{}, 120, {2, 5, 8}] (* Harvey P. Dale, Jun 22 2013 *)
Table[3 Mod[n, 3] + 2, {n, 0, 120}] (* or *)
CoefficientList[Series[(2 + 5 x + 8 x^2)/(1 - x^3), {x, 0, 120}], x]  (* Michael De Vlieger, Jul 02 2016 *)

Prog

(PARI) a(n)=2+3*(n%3) \\ Jaume Oliver Lafont, Mar 24 2009
(Magma) &cat [[2, 5, 8]^^30]; // Wesley Ivan Hurt, Jul 01 2016

Crossrefs

Cf. A177972 (decimal expansion of (85+sqrt(9029))/82).

Sequence in context: A362590 A248510 A020772 * A220337 A198545 A296430

Adjacent sequences: A131595 A131596 A131597 * A131599 A131600 A131601

Keyword

nonn,easy

Author

Paul Curtz, Oct 02 2007

Status

approved