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A037604 Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 1,2,3.

%I A037604 #30 May 07 2023 18:06:57
%S A037604 1,6,27,109,438,1755,7021,28086,112347,449389,1797558,7190235,
%T A037604 28760941,115043766,460175067,1840700269,7362801078,29451204315,
%U A037604 117804817261,471219269046,1884877076187,7539508304749,30158033218998
%N A037604 Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 1,2,3.
%C A037604 Convolution of A000302 with A010882. - _Philippe Deléham_, Mar 24 2013
%H A037604 Michael De Vlieger, <a href="/A037604/b037604.txt">Table of n, a(n) for n = 1..1661</a>
%H A037604 <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,1,-4).
%H A037604 <a href="/index/Ar#2-automatic">Index entries for 2-automatic sequences</a>.
%F A037604 G.f.: x*(1+2x+3*x^2)/((1-x)*(1-4x)*(1+x+x^2)). - _Philippe Deléham_, Mar 24 2013
%F A037604 a(n) = 4*a(n-1) + a(n-3) -4*a(n-4) for n > 5, a(1) = 1, a(2) = 6, a(3) = 27, a(4) = 109, a(5) = 438. - _Philippe Deléham_, Mar 24 2013
%F A037604 a(n+2) = 6*A033140(n) + A191597(n+2). - _Philippe Deléham_, Mar 24 2013
%F A037604 A007090(a(n)) = A037610(n). - _R. J. Mathar_, Apr 27 2015
%F A037604 a(n) = floor(3*4^n/7). - _Karl V. Keller, Jr._, Mar 18 2021
%t A037604 Rest@ CoefficientList[Series[x (1 + 2 x + 3 x^2)/((1 - x) (1 - 4 x) (1 + x + x^2)), {x, 0, 23}], x] (* _Michael De Vlieger_, Mar 19 2021 *)
%t A037604 Table[FromDigits[PadRight[{},n,{1,2,3}],4],{n,30}] (* or *) LinearRecurrence[{4,0,1,-4},{1,6,27,109},30] (* _Harvey P. Dale_, May 07 2023 *)
%o A037604 (PARI) a(n)=([0,1,0,0; 0,0,1,0; 0,0,0,1; -4,1,0,4]^(n-1)*[1;6;27;109])[1,1] \\ _Charles R Greathouse IV_, Feb 13 2017
%o A037604 (Python) print([3*4**n//7 for n in range(1,24)]) # _Karl V. Keller, Jr._, Mar 18 2021
%Y A037604 Cf. A000302, A010882.
%K A037604 nonn,base,easy
%O A037604 1,2
%A A037604 _Clark Kimberling_