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%I #32 Sep 08 2022 08:44:51
%S 1,6,37,223,1338,8029,48175,289050,1734301,10405807,62434842,
%T 374609053,2247654319,13485925914,80915555485,485493332911,
%U 2912959997466,17477759984797,104866559908783,629199359452698,3775196156716189,22651176940297135,135907061641782810
%N Base-6 digits are, in order, the first n terms of the periodic sequence with initial period 1,0,1.
%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (6,0,1,-6).
%F a(n) = 6*a(n-1) + a(n-3) - 6*a(n-4).
%F a(n) = round( (37/215)*6^n ). - _Tani Akinari_, Jul 15 2014
%F G.f.: x*(x^2+1) / ((x-1)*(6*x-1)*(x^2+x+1)). - _Colin Barker_, Jul 15 2014
%e The first six terms have base 6 representations 1, 10, 101, 1011, 10110, 101101. - _Michel Marcus_, Jul 17 2014
%p A033124 := proc(n)
%p coeftayl( (x*(x^2+1) / ((x-1)*(6*x-1)*(x^2+x+1)), x=0, n));
%p end proc:
%p seq(A033124(n), n=1..30); # _Wesley Ivan Hurt_, Jul 17 2014
%t CoefficientList[Series[(x^2 + 1)/((x - 1)*(6*x - 1)*(x^2 + x + 1)), {x, 0, 30}], x] (* _Wesley Ivan Hurt_, Jul 17 2014 *)
%o (PARI) Vec(x*(x^2+1)/((x-1)*(6*x-1)*(x^2+x+1)) + O(x^100)) \\ _Colin Barker_, Jul 15 2014
%o (Magma) [Round((37/215)*6^n) : n in [1..30]]; // _Wesley Ivan Hurt_, Jul 17 2014
%Y Cf. A033128 (similar in base 10).
%K nonn,base,easy
%O 1,2
%A _Clark Kimberling_
%E More terms from _Colin Barker_, Jul 15 2014
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