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%I #26 Jan 15 2023 09:52:47
%S 1,10,71,500,3501,24510,171571,1201000,8407001,58849010,411943071,
%T 2883601500,20185210501,141296473510,989075314571,6923527202000,
%U 48464690414001,339252832898010,2374769830286071,16623388812002500,116363721684017501,814546051788122510
%N Base 7 digits are, in order, the first n terms of the periodic sequence with initial period 1,3.
%H Vincenzo Librandi, <a href="/A037579/b037579.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 (7,1,-7).
%F a(n) = (5*7^n-3*(-1)^(n-1)-8)/24. a(n) = 7*a(n-1)+a(n-2)-7*a(n-3). G.f.: x*(3*x+1) / ((x-1)*(x+1)*(7*x-1)). - _Colin Barker_, Dec 27 2012; corrected Apr 30 2014
%p A037579:=n->(5*7^n-3*(-1)^(n-1)-8)/24; seq(A037579(n), n=1..30); # _Wesley Ivan Hurt_, Apr 29 2014
%t CoefficientList[Series[(3 x + 1)/((x - 1) (x + 1) (7 x - 1)), {x, 0, 30}], x] (* _Vincenzo Librandi_, Oct 22 2013 *)
%t Table[FromDigits[PadRight[{},n,{1,3}],7],{n,30}] (* or *) LinearRecurrence[ {7,1,-7},{1,10,71},30] (* _Harvey P. Dale_, Dec 29 2019 *)
%o (Magma) [(5*7^n-3*(-1)^(n-1)-8)/24: n in [1..30]]; // _Vincenzo Librandi_, Oct 22 2013
%K nonn,base,easy
%O 1,2
%A _Clark Kimberling_, Dec 11 1999
%E More terms from _Colin Barker_, Dec 27 2012
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