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A102865 Base-4 digits are, in order, the first n terms of the sequence (1, 3, 21, 203, 2021, 20203, 202021, 2020203, 20202021, 202020203, ... ). 1

%I

%S 1,3,9,35,137,547,2185,8739,34953,139811,559241,2236963,8947849,

%T 35791395,143165577,572662307,2290649225,9162596899,36650387593,

%U 146601550371,586406201481,2345624805923,9382499223689,37529996894755,150119987579017,600479950316067

%N Base-4 digits are, in order, the first n terms of the sequence (1, 3, 21, 203, 2021, 20203, 202021, 2020203, 20202021, 202020203, ... ).

%H <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (4,1,-4).

%F 4^n = a(n) + A037576(n) for n >= 1.

%F a(n) + a(n+1) = A039301(n+2).

%F a(n) = 4*a(n-1) + a(n-2) - 4*a(n-3). - _Harvey P. Dale_, Mar 23 2012

%F G.f.: 1 + x*(3-3*x-4*x^2)/((1-x)*(1+x)*(1-4*x)). - _Colin Barker_, Aug 28 2012

%t FromDigits[IntegerDigits[#],4]&/@(NestList[FromDigits[Flatten[ IntegerDigits[#]/.{3->{2,1},1->{0,3}}]]&,1,30]) (* or *) LinearRecurrence[{4,1,-4},{1,3,9},31](* _Harvey P. Dale_, Mar 23 2012 *)

%Y Cf. A037576.

%K base,easy,nonn

%O 0,2

%A _Creighton Dement_, Mar 01 2005

%E More terms from _Harvey P. Dale_, Mar 23 2012

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Last modified June 24 18:46 EDT 2021. Contains 345419 sequences. (Running on oeis4.)