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%I #22 Mar 18 2024 13:09:43
%S 1,1,1,1,3,3,3,3,9,9,9,9,27,27,27,27,81,81,81,81,243,243,243,243,729,
%T 729,729,729,2187,2187,2187,2187,6561,6561,6561,6561,19683,19683,
%U 19683,19683,59049,59049,59049,59049,177147,177147,177147,177147,531441
%N Powers of 3 repeated four times.
%C Generating sequence for the number of 0's and 1's (run lengths) in the parity of A006072, A111065 and A118594.
%H Vincenzo Librandi, <a href="/A111575/b111575.txt">Table of n, a(n) for n = 0..8000</a>
%H <a href="/index/Rec#order_04">Index entries for linear recurrences with constant coefficients</a>, signature (0, 0, 0, 3).
%F a(n) = 3^floor(n/4).
%F O.g.f.: -(1+x)*(1+x^2)/(-1+3*x^4). - _R. J. Mathar_, Jan 08 2008
%e a(10) = 3^floor(10/4) = 3^2 = 9.
%t With[{pt=3^Range[0,15]},Sort[Join[pt,pt,pt,pt]]] (* _Harvey P. Dale_, Sep 17 2011 *)
%t Table[PadRight[{},4,3^n],{n,0,15}]//Flatten (* _Harvey P. Dale_, Jan 17 2019 *)
%o (Magma) [3^(Floor(n/4)):n in [0..50]]; // _Vincenzo Librandi_, Sep 20 2011
%o (PARI) a(n)=3^(n\4) \\ _Charles R Greathouse IV_, Oct 03 2016
%Y Cf. A006072, A111065, A108411, A118594, A127975.
%K nonn,easy
%O 0,5
%A _Jeremy Gardiner_, Nov 17 2005
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