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A009983 Powers of 39.

%I A009983 #42 Jul 10 2025 04:13:54
%S A009983 1,39,1521,59319,2313441,90224199,3518743761,137231006679,
%T A009983 5352009260481,208728361158759,8140406085191601,317475837322472439,
%U A009983 12381557655576425121,482880748567480579719,18832349194131742609041,734461618571137961752599,28644003124274380508351361
%N A009983 Powers of 39.
%C A009983 Same as Pisot sequences E(1, 39), L(1, 39), P(1, 39), T(1, 39). Essentially same as Pisot sequences E(39, 1521), L(39, 1521), P(39, 1521), T(39, 1521). See A008776 for definitions of Pisot sequences.
%C A009983 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 39-colored compositions of n such that no adjacent parts have the same color. - _Milan Janjic_, Nov 17 2011
%H A009983 T. D. Noe, <a href="/A009983/b009983.txt">Table of n, a(n) for n = 0..100</a>
%H A009983 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A009983 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (39).
%F A009983 G.f.: 1/(1-39*x). - _Philippe Deléham_, Nov 24 2008
%F A009983 a(n) = 39^n; a(n) = 39*a(n-1), a(0)=1. - _Vincenzo Librandi_, Nov 21 2010
%F A009983 From _Elmo R. Oliveira_, Jul 09 2025: (Start)
%F A009983 E.g.f.: exp(39*x).
%F A009983 a(n) = A063941(n)/17 = A000244(n)*A001022(n). (End)
%t A009983 39^Range[0,20] (* _Harvey P. Dale_, Dec 02 2010 *)
%o A009983 (Magma)[39^n: n in [0..20]]; // _Vincenzo Librandi_, Nov 21 2010
%o A009983 (PARI) a(n)=39^n \\ _Charles R Greathouse IV_, Nov 18 2011
%Y A009983 Cf. A000244, A001022, A008776, A063941.
%K A009983 nonn,easy
%O A009983 0,2
%A A009983 _N. J. A. Sloane_