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%I #26 Dec 14 2023 05:33:57
%S 1,12,123,1230,12301,123012,1230123,12301230,123012301,1230123012,
%T 12301230123,123012301230,1230123012301,12301230123012,
%U 123012301230123,1230123012301230,12301230123012301,123012301230123012,1230123012301230123,12301230123012301230
%N Decimal expansion of a(n) is given by the first n terms of the periodic sequence with initial period 1,2,3,0.
%H <a href="/index/Rec#order_05">Index entries for linear recurrences with constant coefficients</a>, signature (10,0,0,1,-10).
%F a(0)=1, a(1)=12, a(2)=123, a(3)=1230, a(4)=12301, a(n) = 10*a(n-1) + a(n-4) - 10*a(n-5). - _Harvey P. Dale_, Jun 07 2011
%F G.f.: x*(1+2*x+3*x^2) / ( (x-1)*(10*x-1)*(1+x)*(x^2+1) ). - _R. J. Mathar_, Aug 12 2013
%t Rest[RecurrenceTable[{a[0]==0, a[n]==10a[n-1]+Mod[n,4]},a[n], {n,20}]] (* or *) LinearRecurrence[{10,0,0,1,-10},{1,12,123,1230,12301},20] (* _Harvey P. Dale_, Jun 07 2011 *)
%o (PARI) Vec(x*(1+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 1,2
%A _Clark Kimberling_
%E More terms from _Harvey P. Dale_, Jun 07 2011
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