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A146325 Period 3: repeat [1, 4, 1]. 1
1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1, 4, 1, 1 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Continued fraction of (1 + sqrt(26))/5.

Digital roots of the centered triangular numbers A005448(n). - Ant King, May 08 2012

LINKS

Table of n, a(n) for n=1..100.

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

FORMULA

a(n) = 4*(cos((2*n - 1)*arctan(sqrt(3))))^2 = 4 - 4*(sin((2*n - 1)*arctan(sqrt(3))))^2.

a(n+3) = a(n).

a(n) = 2 - cos(2*Pi*n/3) + sqrt(3)*sin(2*Pi*n/3).

O.g.f.: f(x) = a(0) + a(1)*x + ... = (1+4*x+x^2)/(1-x^3) with offset 0. [Richard Choulet, Nov 03 2008]

a(n) = (1/3)*(2*(n mod 3)+5*((n+1) mod 3)-((n+2) mod 3)) with n>=0. [Paolo P. Lava, Nov 06 2008]

a(n) = a(n-3)^(a(n-2)/a(n-1)) with n>3, a(1)=1, a(2)=4, a(3)=1. [Paolo P. Lava, Apr 14 2010]

a(n) = 6 - a(n-1) - a(n-2) for n>2. - Ant King, Jun 12 2012

a(n) = (n mod 3)^(n mod 3). - Bruno Berselli, Jun 27 2016

a(n) = 1 + A021337(n) for n>0. - Wesley Ivan Hurt, Jul 01 2016

MAPLE

seq(op([1, 4, 1]), n=1..50); # Wesley Ivan Hurt, Jul 01 2016

MATHEMATICA

Table[Round[N[4 (Cos[(2 n - 1) ArcTan[Sqrt[3]]])^2, 100]], {n, 1, 100}]

PadLeft[{}, 111, {1, 4, 1}] (* Harvey P. Dale, Sep 18 2011 *)

PROG

(PARI) a(n)=1+3*(n%3==2) \\ Jaume Oliver Lafont, Mar 24 2009

(MAGMA) &cat [[1, 4, 1]^^40]; // Bruno Berselli, Jun 27 2016

CROSSREFS

Cf. A005448, A021337, A131534 (square roots).

Sequence in context: A255511 A014518 A316584 * A069289 A097322 A177023

Adjacent sequences:  A146322 A146323 A146324 * A146326 A146327 A146328

KEYWORD

nonn,easy

AUTHOR

Artur Jasinski, Oct 30 2008

STATUS

approved

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Last modified July 19 04:25 EDT 2019. Contains 325144 sequences. (Running on oeis4.)