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A009971 Powers of 27.

%I A009971 #48 Jul 10 2025 08:13:04
%S A009971 1,27,729,19683,531441,14348907,387420489,10460353203,282429536481,
%T A009971 7625597484987,205891132094649,5559060566555523,150094635296999121,
%U A009971 4052555153018976267,109418989131512359209,2954312706550833698643,79766443076872509863361,2153693963075557766310747
%N A009971 Powers of 27.
%C A009971 Same as Pisot sequences E(1, 27), L(1, 27), P(1, 27), T(1, 27). Essentially same as Pisot sequences E(27, 729), L(27, 729), P(27, 729), T(27, 729). See A008776 for definitions of Pisot sequences.
%C A009971 The compositions of n in which each natural number is colored by one of p different colors are called p-colored compositions of n. For n >= 1, a(n) equals the number of 27-colored compositions of n such that no adjacent parts have the same color. - _Milan Janjic_, Nov 17 2011
%H A009971 T. D. Noe, <a href="/A009971/b009971.txt">Table of n, a(n) for n = 0..100</a>
%H A009971 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A009971 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (27).
%F A009971 G.f.: 1/(1-27*x). - _Philippe Deléham_, Nov 24 2008
%F A009971 a(n) = 27^n; a(n) = 27*a(n-1), n > 0; a(0)=1. - _Vincenzo Librandi_, Nov 21 2010
%F A009971 From _Elmo R. Oliveira_, Jul 10 2025: (Start)
%F A009971 E.g.f.: exp(27*x).
%F A009971 a(n) = A000244(n)*A001019(n) = A000244(A008585(n)). (End)
%t A009971 27^Range[0, 20] (* _Paolo Xausa_, Jul 19 2024 *)
%o A009971 (Sage) [lucas_number1(n,27,0) for n in range(1, 17)] # _Zerinvary Lajos_, Apr 29 2009
%o A009971 (Magma) [27^n: n in [0..100]]; // _Vincenzo Librandi_, Nov 21 2010
%o A009971 (PARI) a(n)=27^n \\ _Charles R Greathouse IV_, Sep 24 2015
%Y A009971 Cf. A000244, A001019, A008585, A008776.
%K A009971 nonn,easy
%O A009971 0,2
%A A009971 _N. J. A. Sloane_