%I #46 Jul 12 2023 12:45:43

%S 1,41,1681,68921,2825761,115856201,4750104241,194754273881,

%T 7984925229121,327381934393961,13422659310152401,550329031716248441,

%U 22563490300366186081,925103102315013629321,37929227194915558802161

%N Powers of 41.

%C Same as Pisot sequences E(1, 41), L(1, 41), P(1, 41), T(1, 41). Essentially same as Pisot sequences E(41, 1681), L(41, 1681), P(41, 1681), T(41, 1681). 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 41-colored compositions of n such that no adjacent parts have the same color. - _Milan Janjic_, Nov 17 2011

%C Numbers n such that sigma(41*n) = 41*n + sigma(n). - _Jahangeer Kholdi_, Nov 23 2013

%H T. D. Noe, <a href="/A009985/b009985.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 (41).

%F G.f.: 1/(1-41*x). - _Philippe Deléham_, Nov 24 2008

%F a(n) = 41^n; a(n) = 41*a(n-1), a(0)=1. - _Vincenzo Librandi_, Nov 21 2010

%t 41^Range[0, 14] (* _Alonso del Arte_, Sep 04 2015 *)

%t NestList[41#&,1,20] (* _Harvey P. Dale_, Mar 07 2017 *)

%o (Magma)[41^n: n in [0..20]]; // _Vincenzo Librandi_, Nov 21 2010

%o (PARI) first(m)=vector(m,i,i--;41^i) \\ _Anders Hellström_, Sep 12 2015

%K nonn,easy

%O 0,2

%A _N. J. A. Sloane_