A154815 Period 6: repeat [8, 7, 4, 5, 2, 1].

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

Offset: 0

Author

Paul Curtz, Jan 15 2009

Keywords

• nonn
• easy

Comments

Obtained through reversion of the period in A153990, or by taking a half period of A154811.

Shares digits with other 6-periodic sequences, see the list in A153130.

Also the decimal expansion of the constant 97169/111111. [R. J. Mathar, Jan 23 2009]

Links

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

Crossrefs

Cf. A153130, A153990, A154811.

Programs

Magma

&cat [[8, 7, 4, 5, 2, 1]^^20]; // Wesley Ivan Hurt, Jun 23 2016

Maple

A154815:=n->[8, 7, 4, 5, 2, 1][(n mod 6)+1]: seq(A154815(n), n=0..100); # Wesley Ivan Hurt, Jun 23 2016

Mathematica

PadRight[{}, 100, {8, 7, 4, 5, 2, 1}] (* Wesley Ivan Hurt, Jun 23 2016 *)

Formula

a(n) = (8*A153990(n)) mod 9.

G.f.: (8+7*x+4*x^2+5*x^3+2*x^4+x^5)/((1-x)*(1+x)*(1+x+x^2)(x^2-x+1)). [R. J. Mathar, Jan 23 2009]

From Wesley Ivan Hurt, Jun 23 2016: (Start)

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

a(n) = (27 + cos(n*Pi) + 8*cos(n*Pi/3) + 12*cos(2*n*Pi/3) + 8*sqrt(3)*sin(n*Pi/3) + 4*sqrt(3)*sin(2*n*Pi/3))/6. (End)

Extensions

Edited by R. J. Mathar, Jan 23 2009