A105899 Period 6: repeat [1, 1, 2, 2, 3, 3].

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

Offset

0,3

Links

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

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

Formula

G.f.: -(3*x^4+2*x^2+1)/(x-1)/(x^2+x+1)/(x^2-x+1). a(n) = A131555(n)+1. - R. J. Mathar, Nov 14 2007

From Wesley Ivan Hurt, Jun 17 2016: (Start)

a(n) = a(n-1) - a(n-2) + a(n-3) - a(n-4) + a(n-5) for n>4.

a(n) = (12-2*sqrt(3)*cos((1-4*n)*Pi/6)-6*sin((1+2*n)*Pi/6))/6. (End)

a(n) = floor(n/2) - 3*floor(n/6) + 1. - Ridouane Oudra, Sep 09 2023

Maple

A105899:=n->(12-2*sqrt(3)*cos((1-4*n)*Pi/6)-6*sin((1+2*n)*Pi/6))/6: seq(A105899(n), n=0..100); # Wesley Ivan Hurt, Jun 17 2016

Mathematica

Flatten[Table[{1, 1, 2, 2, 3, 3}, {20}]] (* Wesley Ivan Hurt, Jun 17 2016 *)
PadRight[{}, 120, {1, 1, 2, 2, 3, 3}] (* Harvey P. Dale, May 09 2022 *)

Prog

(PARI) a(n)=1+n%6\2 \\ Jaume Oliver Lafont, Aug 30 2009
(Magma) &cat[[1, 1, 2, 2, 3, 3]: n in [0..20]]; // Wesley Ivan Hurt, Jun 17 2016

Crossrefs

Cf. A131555.

Cf. A178308 Decimal expansion of (111+sqrt(25277))/158. [Klaus Brockhaus, May 24 2010]

Sequence in context: A288723 A071859 A135695 * A071434 A366549 A227314

Adjacent sequences: A105896 A105897 A105898 * A105900 A105901 A105902

Keyword

nonn,easy,less

Author

Paul Curtz, Aug 27 2007

Extensions

Edited by N. J. A. Sloane, Sep 15 2007

More terms from Klaus Brockhaus, May 24 2010

Status

approved