A153990 Period 6: repeat [1, 2, 5, 4, 7, 8].

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

Offset: 0

Author

Paul Curtz, Jan 04 2009

Keywords

• nonn
• easy
• less

Comments

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

Also the decimal expansion of the constant 13942/111111. [R. J. Mathar, Jan 23 2009]

Links

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

Crossrefs

Cf. A131533, A141425, A153130, A154811.

Programs

Magma

&cat[[1, 2, 5, 4, 7, 8]: n in [0..20]]; // Wesley Ivan Hurt, Jun 17 2016

Maple

A153990:=n->(27-cos(n*Pi)-8*sqrt(3)*cos((1-4*n)*Pi/6)-16*sin((1+2*n)*Pi/6))/6: seq(A153990(n), n=0..100); # Wesley Ivan Hurt, Jun 17 2016

Mathematica

Flatten[Table[{1, 2, 5, 4, 7, 8}, {20}]] (* Wesley Ivan Hurt, Jun 17 2016 *)
PadRight[{},120,{1,2,5,4,7,8}] (* Harvey P. Dale, Nov 08 2017 *)

Formula

a(n) - A141425(n) = A131533(n+2).

a(6n+0) + a(6n+5) = a(6n+1) + a(6n+4) = a(6n+2) + a(6n+3) = 9.

G.f.: (1+2*x+5*x^2+4*x^3+7*x^4+8*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 17 2016: (Start)

a(n) = (27-cos(n*Pi)-8*sqrt(3)*cos((1-4*n)*Pi/6)-16*sin((1+2*n)*Pi/6))/6.

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

Extensions

Edited by R. J. Mathar, Jan 23 2009