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%I #21 Oct 25 2023 10:02:51
%S 1,12,109,984,8857,79716,717445,6457008,58113073,523017660,4707158941,
%T 42364430472,381279874249,3431518868244,30883669814197,
%U 277953028327776,2501577254949985,22514195294549868,202627757650948813,1823649818858539320,16412848369726853881
%N Base 9 digits are, in order, the first n terms of the periodic sequence with initial period 1,3.
%H Vincenzo Librandi, <a href="/A037581/b037581.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (9,1,-9).
%F From _Colin Barker_, Dec 27 2012: (Start)
%F a(n) = (3^(1+2*n) + 2*(-1)^n - 5)/20.
%F a(n) = 9*a(n-1) + a(n-2) - 9*a(n-3).
%F G.f.: x*(3*x+1) / ((x-1)*(x+1)*(9*x-1)). (End)
%F E.g.f.: (3*(cosh(9*x) - cosh(x) + sinh(9*x)) - 7*sinh(x))/20. - _Stefano Spezia_, Oct 25 2023
%t CoefficientList[Series[(3 x + 1)/((x - 1) (x + 1) (9 x - 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 22 2013 *)
%t Module[{nn=30,d},d=PadRight[{},nn,{1,3}];Table[FromDigits[Take[d,n],9],{n,nn}]] (* _Harvey P. Dale_, Jul 22 2015 *)
%o (Magma) [(3^(1+2*n)+2*(-1)^n-5)/20: n in [1..30]]; // _Vincenzo Librandi_, Oct 22 2013
%K nonn,base,easy
%O 1,2
%A _Clark Kimberling_
%E More terms from _Colin Barker_, Dec 27 2012
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