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%I #31 Feb 19 2024 01:51:33
%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]
%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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