A154815 - OEIS

%I #15 Mar 15 2024 02:22:54

%S 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,

%T 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,

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

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

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

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

%C Also the decimal expansion of the constant 97169/111111. [_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) = (8*A153990(n)) mod 9.

%F 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]

%F From _Wesley Ivan Hurt_, Jun 23 2016: (Start)

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

%F 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)

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

%t PadRight[{}, 100, {8, 7, 4, 5, 2, 1}] (* _Wesley Ivan Hurt_, Jun 23 2016 *)

%o (Magma) &cat [[8, 7, 4, 5, 2, 1]^^20]; // _Wesley Ivan Hurt_, Jun 23 2016

%Y Cf. A153130, A153990, A154811.

%K nonn,easy

%O 0,1

%A _Paul Curtz_, Jan 15 2009

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