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A037480 Base-3 digits are, in order, the first n terms of the periodic sequence with initial period 1,2. 3

%I #27 Dec 15 2019 13:24:05

%S 1,5,16,50,151,455,1366,4100,12301,36905,110716,332150,996451,2989355,

%T 8968066,26904200,80712601,242137805,726413416,2179240250,6537720751,

%U 19613162255,58839486766,176518460300,529555380901

%N Base-3 digits are, in order, the first n terms of the periodic sequence with initial period 1,2.

%H Vincenzo Librandi, <a href="/A037480/b037480.txt">Table of n, a(n) for n = 1..200</a>

%H <a href="/index/Rec">Index entries for linear recurrences with constant coefficients</a>, signature (3,1,-3).

%F a(n) = (5*3^n + (-1)^n - 6)/8 . - _Paul D. Hanna_, Sep 23 2007

%F a(n) = 3*a(n-1)+a(n-2)-3*a(n-3). G.f.: x*(2*x+1) / ((x-1)*(x+1)*(3*x-1)). - _Colin Barker_, Apr 30 2014

%p a[0]:=0:a[1]:=1:for n from 2 to 50 do a[n]:=2*a[n-1]+3*a[n-2]+3 od: seq(a[n], n=1..33); # _Zerinvary Lajos_, Dec 14 2008

%t CoefficientList[Series[(2 x + 1)/((x - 1) (x + 1) (3 x - 1)), {x, 0, 40}], x] (* _Vincenzo Librandi_, May 01 2014 *)

%t Table[FromDigits[PadRight[{},n,{1,2}],3],{n,30}] (* or *) LinearRecurrence[ {3,1,-3},{1,5,16},30] (* _Harvey P. Dale_, Dec 15 2019 *)

%o (PARI) Vec(x*(2*x+1)/((x-1)*(x+1)*(3*x-1)) + O(x^100)) \\ _Colin Barker_, Apr 30 2014

%K nonn,base,easy

%O 1,2

%A _Clark Kimberling_

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Last modified March 29 02:23 EDT 2024. Contains 371264 sequences. (Running on oeis4.)