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Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 2,1,3,0.
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%I #20 Dec 14 2023 05:31:09

%S 2,21,213,2130,21302,213021,2130213,21302130,213021302,2130213021,

%T 21302130213,213021302130,2130213021302,21302130213021,

%U 213021302130213,2130213021302130,21302130213021302,213021302130213021,2130213021302130213,21302130213021302130

%N Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 2,1,3,0.

%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (10,0,0,1,-10).

%F a(n) = 10*a(n-1) + a(n-4) - 10*a(n-5). G.f.: x*(2+x+3*x^2) / ((x-1)*(10*x-1)*(1+x)*(x^2+1)). - _R. J. Mathar_, Oct 05 2009

%t nn=10;With[{c=PadLeft[{},4nn,{2,1,3,0}]},Table[FromDigits[Take[c,n]], {n,4nn}]] (* _Harvey P. Dale_, Aug 16 2011 *)

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

%K nonn,base,easy

%O 1,1

%A _Clark Kimberling_

%E More terms from _Harvey P. Dale_, Aug 16 2011