%I #18 Aug 05 2017 05:46:11
%S 3,19,118,709,4259,25557,153343,920062,5520373,33122243,198733461,
%T 1192400767,7154404606,42926427637,257558565827,1545351394965,
%U 9272108369791,55632650218750,333795901312501,2002775407875011,12016652447250069,72099914683500415
%N Base 6 digits are, in order, the first n terms of the periodic sequence with initial period 3,1,4,1,5 (the first five digits of Pi).
%H Colin Barker, <a href="/A290477/b290477.txt">Table of n, a(n) for n = 1..1000</a>
%H <a href="/index/Rec#order_06">Index entries for linear recurrences with constant coefficients</a>, signature (6,0,0,0,1,-6).
%F From _Colin Barker_, Aug 04 2017: (Start)
%F G.f.: x*(3 + x + 4*x^2 + x^3 + 5*x^4) / ((1 - x)*(1 - 6*x)*(1 + x + x^2 + x^3 + x^4)).
%F a(n) = 6*a(n-1) + a(n-5) - 6*a(n-6) for n>6.
%F (End)
%e Base 6...........Decimal
%e 3......................3
%e 31....................19
%e 314..................118
%e 3141.................709
%e 31415...............4259
%e 314153.............25557
%e 3141531...........153343
%e etc. - _Colin Barker_, Aug 04 2017
%t Table[FromDigits[PadRight[{},n,{3,1,4,1,5}],6],{n,30}] (* or *) LinearRecurrence[{6,0,0,0,1,-6},{3,19,118,709,4259,25557},30]
%o (PARI) Vec(x*(3 + x + 4*x^2 + x^3 + 5*x^4) / ((1 - x)*(1 - 6*x)*(1 + x + x^2 + x^3 + x^4)) + O(x^30)) \\ _Colin Barker_, Aug 04 2017
%K nonn,base,easy
%O 1,1
%A _Harvey P. Dale_, Aug 03 2017
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