A130815 Period 6: repeat [1, 5, 4, -1, -5, -4].

1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4, 1, 5, 4, -1, -5, -4

Offset: 0

Author

Paul Curtz, Jul 16 2007

Keywords

• sign
• easy
• less

Comments

Continued fraction expansion of (5+sqrt(11))/7 = 1.1880892557650... - R. J. Mathar, Mar 08 2012

Links

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

Crossrefs

Cf. A010892.

Programs

Magma

&cat[[1, 5, 4, -1, -5, -4]: n in [0..20]]; // Wesley Ivan Hurt, Jun 17 2016

Mathematica

Flatten[Table[{1, 5, 4, -1, -5, -4}, {20}]] (* Wesley Ivan Hurt, Jun 17 2016 *)
PadRight[{},120,{1,5,4,-1,-5,-4}] (* Harvey P. Dale, Jul 12 2020 *)

PARI

a(n)=[1,5,4,-1,-5,-4][n%6+1] \\ Charles R Greathouse IV, Jun 02 2011

Formula

Binomial transform of 1, 4, -5.

From R. J. Mathar, Oct 30 2008: (Start)

G.f.: (1+4x)/(1-x+x^2).

a(n) = A010892(n) + 4*A010892(n-1). (End)

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

a(n) = a(n-1) - a(n-2) for n>1.

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

Extensions

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