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Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 2,0,3.
3

%I #24 Jul 29 2024 12:07:12

%S 2,20,203,2032,20320,203203,2032032,20320320,203203203,2032032032,

%T 20320320320,203203203203,2032032032032,20320320320320,

%U 203203203203203,2032032032032032,20320320320320320,203203203203203203,2032032032032032032,20320320320320320320

%N Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 2,0,3.

%H Vincenzo Librandi, <a href="/A037624/b037624.txt">Table of n, a(n) for n = 1..200</a>

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

%t CoefficientList[Series[(2 + 3 x^2) / ((x - 1) (10 x - 1) (1 + x + x^2)), {x, 0, 20}], x] (* _Vincenzo Librandi_, Feb 16 2018 *)

%t Table[FromDigits[PadRight[{},n,{2,0,3}]],{n,20}] (* _Harvey P. Dale_, Jul 29 2024 *)

%o (Magma) I:=[2,20,203,2032]; [n le 4 select I[n] else 10*Self(n-1)+Self(n-3)-10*Self(n-4): n in [1..30]]; // _Vincenzo Librandi_, Feb 16 2018

%K nonn,base

%O 1,1

%A _Clark Kimberling_