OFFSET
1,2
COMMENTS
Continued fraction of (1 + sqrt(26))/5 = A188659.
Also the digital roots of centered 12-gonal numbers A003154. - Peter M. Chema, Dec 20 2023
LINKS
FORMULA
a(n) = 4*(cos((2*n - 1)*Pi/3))^2 = 4 - 4*(sin((2*n - 1)*Pi/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.: x*(1+4*x+x^2)/(1-x^3). [Richard Choulet, Nov 03 2008]
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
KEYWORD
nonn,easy
AUTHOR
Artur Jasinski, Oct 30 2008
STATUS
approved