%I #40 Oct 03 2023 09:59:46
%S 1,7,28,113,455,1820,7281,29127,116508,466033,1864135,7456540,
%T 29826161,119304647,477218588,1908874353,7635497415,30541989660,
%U 122167958641,488671834567,1954687338268,7818749353073,31274997412295
%N Base-4 digits are, in order, the first n terms of the periodic sequence with initial period 1,3,0.
%H Vincenzo Librandi, <a href="/A037597/b037597.txt">Table of n, a(n) for n = 1..300</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (4,0,1,-4).
%F a(n) = floor(4^(n+1)/9). - _Mircea Merca_, Dec 26 2010
%F From _Joerg Arndt_, Jan 08 2011: (Start)
%F G.f.: x*(1+3*x) / ( (x-1)*(4*x-1)*(1+x+x^2) ).
%F a(n) = 4*a(n-1) + a(n-3) - 4*a(n-4). (End)
%F a(1)=1, a(2)=7, a(n) = 5*a(n-1) - 4*a(n-2) + (period 3: repeat -3, 1, 2). - _Vincenzo Librandi_, Jun 06 2011
%F E.g.f.: 2*(2*exp(x)*(exp(3*x) - 1) - sqrt(3)*exp(-x/2)*sin(sqrt(3)*x/x))/9. - _Stefano Spezia_, Oct 02 2023
%p seq(floor(4^(n+1)/9),n=1..32); # _Mircea Merca_, Dec 28 2010
%o (Magma) [Floor(4^(n+1)/9): n in [1..30]]; // _Vincenzo Librandi_, May 22 2011
%o (PARI) a(n)=4^(n+1)\9 \\ _Charles R Greathouse IV_, Jun 06 2011
%Y Cf. A178744.
%K nonn,base,easy
%O 1,2
%A _Clark Kimberling_