%I #24 Mar 08 2024 11:57:55

%S 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,

%T 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,

%U 5,4,7,8,1,2,5,4,7,8,1,2,5,4,7,8,1,2

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

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

%C Also the decimal expansion of the constant 13942/111111. [_R. J. Mathar_, Jan 23 2009]

%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).

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

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

%F 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]

%F From _Wesley Ivan Hurt_, Jun 17 2016: (Start)

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

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

%p 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

%t Flatten[Table[{1, 2, 5, 4, 7, 8}, {20}]] (* _Wesley Ivan Hurt_, Jun 17 2016 *)

%t PadRight[{},120,{1,2,5,4,7,8}] (* _Harvey P. Dale_, Nov 08 2017 *)

%o (Magma) &cat[[1, 2, 5, 4, 7, 8]: n in [0..20]]; // _Wesley Ivan Hurt_, Jun 17 2016

%Y Cf. A131533, A141425, A153130, A154811.

%K nonn,easy,less

%O 0,2

%A _Paul Curtz_, Jan 04 2009

%E Edited by _R. J. Mathar_, Jan 23 2009