A177883 Period 6: repeat [4, 5, 7, 2, 1, 8].

4, 5, 7, 2, 1, 8, 4, 5, 7, 2, 1, 8, 4, 5, 7, 2, 1, 8, 4, 5, 7, 2, 1, 8, 4, 5, 7, 2, 1, 8, 4, 5, 7, 2, 1, 8, 4, 5, 7, 2, 1, 8, 4, 5, 7, 2, 1, 8, 4, 5, 7, 2, 1, 8, 4, 5, 7, 2, 1, 8, 4, 5, 7, 2, 1, 8, 4, 5, 7, 2, 1, 8, 4, 5, 7, 2, 1, 8, 4, 5, 7, 2, 1, 8, 4, 5

Offset: 0

Author

Paul Curtz, Dec 14 2010

Keywords

• nonn
• easy

Comments

Represents also the decimal expansion of 16934/37037 and the continued fractions of 0.23839... = (sqrt(496555)-667)/158 or of 4.194699... = (667+sqrt(496555))/327. - R. J. Mathar, Dec 20 2010

Links

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

Crossrefs

Cf. A173598, A141425, A153130 (permutations).

Programs

Magma

&cat[[4, 5, 7, 2, 1, 8]: n in [0..20]]; // Wesley Ivan Hurt, Jun 18 2016

Maple

A177883:=n->[4, 5, 7, 2, 1, 8][(n mod 6)+1]: seq(A177883(n), n=0..100); # Wesley Ivan Hurt, Jun 18 2016

Mathematica

PadRight[{}, 120, {4,5,7,2,1,8}] (* Harvey P. Dale, Feb 11 2016 *)

PARI

a(n)=[4, 5, 7, 2, 1, 8][n%6+1] \\ Charles R Greathouse IV, Jul 17 2016

Formula

a(n) = A166304(n) mod 9 = A022998(3n+2) mod 9.

a(2n) + a(2n+1) = 9.

G.f.: (4+5*x+7*x^2+2*x^3+x^4+8*x^5) / ( (1-x)*(1+x)*(1+x+x^2)*(x^2-x+1) ). - R. J. Mathar, Dec 20 2010

From Wesley Ivan Hurt, Jun 18 2016: (Start)

a(n) = a(n-6) for n>5.

a(n) = (9 -cos(n*Pi) + 3*cos(n*Pi/3) - 3*cos(2*n*Pi/3) + sqrt(3)*sin(n*Pi/3) - 3*sqrt(3)*sin(2*n*Pi/3))/2. (End)