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A009986 Powers of 42.

%I A009986 #38 Jul 10 2025 16:04:06
%S A009986 1,42,1764,74088,3111696,130691232,5489031744,230539333248,
%T A009986 9682651996416,406671383849472,17080198121677824,717368321110468608,
%U A009986 30129469486639681536,1265437718438866624512,53148384174432398229504,2232232135326160725639168,93753749683698750476845056
%N A009986 Powers of 42.
%C A009986 Same as Pisot sequences E(1, 42), L(1, 42), P(1, 42), T(1, 42). Essentially same as Pisot sequences E(42, 1764), L(42, 1764), P(42, 1764), T(42, 1764). See A008776 for definitions of Pisot sequences.
%C A009986 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 42-colored compositions of n such that no adjacent parts have the same color. - _Milan Janjic_, Nov 17 2011
%H A009986 T. D. Noe, <a href="/A009986/b009986.txt">Table of n, a(n) for n = 0..100</a>
%H A009986 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>.
%H A009986 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (42).
%F A009986 G.f.: 1/(1-42*x). - _Philippe Deléham_, Nov 24 2008
%F A009986 a(n) = 42^n; a(n) = 42*a(n-1), a(0)=1. - _Vincenzo Librandi_, Nov 21 2010
%F A009986 From _Elmo R. Oliveira_, Jul 10 2025: (Start)
%F A009986 E.g.f.: exp(42*x).
%F A009986 a(n) = A000079(n)*A009965(n) = A000400(n)*A000420(n). (End)
%t A009986 42^Range[0, 14] (* _Michael De Vlieger_, Jan 13 2018 *)
%o A009986 (Magma)[42^n: n in [0..20]]; // _Vincenzo Librandi_, Nov 21 2010
%o A009986 (PARI) a(n) = 42^n; \\ _Michel Marcus_, Jan 14 2018
%Y A009986 Cf. A000079, A000400, A000420, A008776, A009965.
%K A009986 nonn,easy
%O A009986 0,2
%A A009986 _N. J. A. Sloane_