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

%I A153990 #24 Mar 08 2024 11:57:55
%S A153990 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 A153990 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 A153990 5,4,7,8,1,2,5,4,7,8,1,2,5,4,7,8,1,2
%N A153990 Period 6: repeat [1, 2, 5, 4, 7, 8].
%C A153990 Shares digits with other 6-periodic sequences, see the list in A153130.
%C A153990 Also the decimal expansion of the constant 13942/111111. [_R. J. Mathar_, Jan 23 2009]
%H A153990 <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (0,0,0,0,0,1).
%F A153990 a(n) - A141425(n) = A131533(n+2).
%F A153990 a(6n+0) + a(6n+5) = a(6n+1) + a(6n+4) = a(6n+2) + a(6n+3) = 9.
%F A153990 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 A153990 From _Wesley Ivan Hurt_, Jun 17 2016: (Start)
%F A153990 a(n) = (27-cos(n*Pi)-8*sqrt(3)*cos((1-4*n)*Pi/6)-16*sin((1+2*n)*Pi/6))/6.
%F A153990 a(n) = a(n-6) for n>5. (End)
%p A153990 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 A153990 Flatten[Table[{1, 2, 5, 4, 7, 8}, {20}]] (* _Wesley Ivan Hurt_, Jun 17 2016 *)
%t A153990 PadRight[{},120,{1,2,5,4,7,8}] (* _Harvey P. Dale_, Nov 08 2017 *)
%o A153990 (Magma) &cat[[1, 2, 5, 4, 7, 8]: n in [0..20]]; // _Wesley Ivan Hurt_, Jun 17 2016
%Y A153990 Cf. A131533, A141425, A153130, A154811.
%K A153990 nonn,easy,less
%O A153990 0,2
%A A153990 _Paul Curtz_, Jan 04 2009
%E A153990 Edited by _R. J. Mathar_, Jan 23 2009