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A010885 Period 6: repeat [1, 2, 3, 4, 5, 6]. 3

%I

%S 1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,

%T 5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,3,4,5,6,1,2,

%U 3,4,5,6,1,2,3,4,5,6,1,2,3

%N Period 6: repeat [1, 2, 3, 4, 5, 6].

%C Partial sums are given by A130484(n)+n+1. - _Hieronymus Fischer_, Jun 08 2007

%C 41152/333333 = 0.123456123456123456... [_Eric Desbiaux_, Nov 03 2008]

%C Terms of the simple continued fraction of 75/(4*sqrt(4171)-206). [_Paolo P. Lava_, Feb 16 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) = 1 + (n mod 6). - _Paolo P. Lava_, Nov 21 2006

%F a(n) = A010875(n)+1. G.f.: g(x)=(Sum_{0<=k<6} (k+1)*x^k)/(1-x^6). Also g(x)=(6*x^7-7*x^6+1)/((1-x^6)*(1-x)^2). - _Hieronymus Fischer_, Jun 08 2007

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

%F G.f.: (1+2*x+3*x^2+4*x^3+5*x^4+6*x^5)/(1-x^6).

%F a(n) = (21-3*cos(n*Pi)-4*sqrt(3)*cos((1-4*n)*Pi/6)-12*sin((1+2*n)*Pi/6))/6.

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

%p A010885:=n->(21-3*cos(n*Pi)-4*sqrt(3)*cos((1-4*n)*Pi/6)-12*sin((1+2*n)*Pi/6))/6: seq(A010885(n), n=0..100); # _Wesley Ivan Hurt_, Jun 17 2016

%t Flatten[Table[Range[6],{n,15}]] (* _Harvey P. Dale_, Aug 01 2011 *)

%t PadRight[{},90,Range[6]] (* _Harvey P. Dale_, Sep 23 2019 *)

%o (MAGMA) &cat[[1..6]: n in [0..20]]; // _Wesley Ivan Hurt_, Jun 17 2016

%Y Cf. A010872, A010873, A010874, A010875, A010876, A004526, A002264, A002265, A002266.

%Y Cf. A177158 (decimal expansion of (103+2*sqrt(4171))/162). [From _Klaus Brockhaus_, May 03 2010]

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_

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Last modified October 18 07:42 EDT 2019. Contains 328146 sequences. (Running on oeis4.)