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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. 0

%I

%S 1,6,27,109,438,1755,7021,28086,112347,449389,1797558,7190235,

%T 28760941,115043766,460175067,1840700269,7362801078,29451204315,

%U 117804817261,471219269046,1884877076187,7539508304749,30158033218998

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

%C Convolution of A000302 with A010882. - _Philippe Deléham_, Mar 24 2013

%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,1,-4).

%H <a href="/index/Ar#2-automatic">Index entries for 2-automatic sequences</a>.

%F G.f.: x*(1+2x+3*x^2)/((1-x)*(1-4x)*(1+x+x^2)). - _Philippe Deléham_, Mar 24 2013

%F 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 a(n+2) = 6*A033140(n) + A191597(n+2). - _Philippe Deléham_, Mar 24 2013

%F A007090(a(n)) = A037610(n). _R. J. Mathar_, Apr 27 2015

%o (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

%Y Cf. A000302, A010882.

%K nonn,base,easy

%O 1,2

%A _Clark Kimberling_

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Last modified March 25 16:38 EDT 2019. Contains 321474 sequences. (Running on oeis4.)