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Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 2,1,3.
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%I #21 Dec 14 2023 05:39:13

%S 2,21,213,2132,21321,213213,2132132,21321321,213213213,2132132132,

%T 21321321321,213213213213,2132132132132,21321321321321,

%U 213213213213213,2132132132132132

%N Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 2,1,3.

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (10,0,1,-10).

%F G.f.: x*(2+x+3*x^2) / ( (x-1)*(10*x-1)*(1+x+x^2) ). - _R. J. Mathar_, Nov 21 2011

%t Table[FromDigits[PadRight[{},n,{2,1,3}]],{n,20}] (* or *) LinearRecurrence[{10,0,1,-10},{2,21,213,2132},20] (* _Harvey P. Dale_, Jun 23 2016 *)

%o (PARI) Vec(x*(2+x+3*x^2)/((x-1)*(10*x-1)*(1+x+x^2)) + O(x^25)) \\ _Jinyuan Wang_, Apr 14 2020

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_