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%I #48 Jul 12 2023 12:35:57
%S 1,26,676,17576,456976,11881376,308915776,8031810176,208827064576,
%T 5429503678976,141167095653376,3670344486987776,95428956661682176,
%U 2481152873203736576,64509974703297150976,1677259342285725925376,43608742899428874059776,1133827315385150725554176,29479510200013918864408576,766467265200361890474622976,19928148895209409152340197376
%N Powers of 26.
%C Same as Pisot sequences E(1, 26), L(1, 26), P(1, 26), T(1, 26). Essentially same as Pisot sequences E(26, 676), L(26, 676), P(26, 676), T(26, 676). 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 26-colored compositions of n such that no adjacent parts have the same color. - _Milan Janjic_, Nov 17 2011
%C Number of n-letter words over an alphabet with 26 letters. - _Wesley Ivan Hurt_, Apr 17 2016
%H T. D. Noe, <a href="/A009970/b009970.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 (26).
%F G.f.: 1/(1-26*x). - _Philippe Deléham_, Nov 23 2008
%F E.g.f.: exp(26*x). - _Zerinvary Lajos_, Apr 29 2009
%F From _Vincenzo Librandi_, Nov 21 2010: (Start)
%F a(n) = 26*a(n-1) for n > 0, a(0) = 1.
%F a(n) = 26^n. (End)
%p A009970:=n->26^n: seq(A009970(n), n=0..25); # _Wesley Ivan Hurt_, Apr 17 2016
%t 26^Range[0, 25] (* _Alonso del Arte_, Mar 25 2015 *)
%t NestList[26#&,1,20] (* _Harvey P. Dale_, Jan 14 2017 *)
%o (Sage) [lucas_number1(n,26,0) for n in range(1, 17)] # _Zerinvary Lajos_, Apr 29 2009
%o (Magma)[26^n: n in [0..100]] // _Vincenzo Librandi_, Nov 21 2010
%o (Maxima) A009970(n):=26^n$
%o makelist(A009970(n),n,0,30); /* _Martin Ettl_, Nov 07 2012 */
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_
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