%I #34 Jul 12 2023 12:46:16

%S 1,42,1764,74088,3111696,130691232,5489031744,230539333248,

%T 9682651996416,406671383849472,17080198121677824,717368321110468608,

%U 30129469486639681536,1265437718438866624512,53148384174432398229504

%N Powers of 42.

%C 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 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 T. D. Noe, <a href="/A009986/b009986.txt">Table of n, a(n) for n = 0..100</a>

%H Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (42).

%F G.f.: 1/(1-42*x). - _Philippe Deléham_, Nov 24 2008

%F a(n) = 42^n; a(n) = 42*a(n-1), a(0)=1. - _Vincenzo Librandi_, Nov 21 2010

%t 42^Range[0, 14] (* _Michael De Vlieger_, Jan 13 2018 *)

%o (Magma)[42^n: n in [0..20]] // _Vincenzo Librandi_, Nov 21 2010

%o (PARI) a(n) = 42^n; \\ _Michel Marcus_, Jan 14 2018

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_