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A009982 Powers of 38.

%I A009982 #43 Jul 10 2025 10:59:36
%S A009982 1,38,1444,54872,2085136,79235168,3010936384,114415582592,
%T A009982 4347792138496,165216101262848,6278211847988224,238572050223552512,
%U A009982 9065737908494995456,344498040522809827328,13090925539866773438464,497455170514937390661632,18903296479567620845142016
%N A009982 Powers of 38.
%C A009982 Same as Pisot sequences E(1, 38), L(1, 38), P(1, 38), T(1, 38). Essentially same as Pisot sequences E(38, 1444), L(38, 1444), P(38, 1444), T(38, 1444). See A008776 for definitions of Pisot sequences.
%C A009982 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 38-colored compositions of n such that no adjacent parts have the same color. - _Milan Janjic_, Nov 17 2011. [See A000244 for a proof.]
%H A009982 T. D. Noe, <a href="/A009982/b009982.txt">Table of n, a(n) for n=0..100</a>
%H A009982 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A009982 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (38).
%F A009982 G.f.: 1/(1 - 38*x). - _Philippe Deléham_, Nov 24 2008
%F A009982 a(n) = 38^n; a(n) = 38*a(n-1), n > 0, a(0) = 1. - _Vincenzo Librandi_, Nov 21 2010
%F A009982 From _Elmo R. Oliveira_, Jul 10 2025: (Start)
%F A009982 E.g.f.: exp(38*x).
%F A009982 a(n) = A000079(n)*A001029(n). (End)
%t A009982 38^Range[0, 19] (* _Alonso del Arte_, Feb 18 2017 *)
%o A009982 (Magma) [38^n: n in [0..20]]; // _Vincenzo Librandi_, Nov 21 2010
%o A009982 (PARI) a(n)=38^n \\ _M. F. Hasler_, Feb 21 2017
%Y A009982 Cf. A000079, A000244, A001029, A008776.
%K A009982 nonn,easy
%O A009982 0,2
%A A009982 _N. J. A. Sloane_