%I #57 Jul 12 2023 12:34:09
%S 1,24,576,13824,331776,7962624,191102976,4586471424,110075314176,
%T 2641807540224,63403380965376,1521681143169024,36520347436056576,
%U 876488338465357824,21035720123168587776,504857282956046106624,12116574790945106558976,290797794982682557415424,6979147079584381377970176,167499529910025153071284224,4019988717840603673710821376
%N Powers of 24: a(n) = 24^n.
%C Same as Pisot sequences E(1, 24), L(1, 24), P(1, 24), T(1, 24). Essentially same as Pisot sequences E(24, 576), L(24, 576), P(24, 576), T(24, 576). See A008776 for definitions of Pisot sequences.
%C If X_1, X_2, ..., X_n is a partition of the set {1, 2, ..., 2*n} into blocks of size 2 then, for n >= 1, a(n) is equal to the number of functions f : {1, 2, ..., 2*n} -> {1, 2, 3, 4, 5} such that for fixed y_1, y_2, ..., y_n in {1, 2, 3, 4, 5} we have f(X_i) <> {y_i}, (i = 1, 2, ..., n). - _Milan Janjic_, May 24 2007
%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 24-colored compositions of n such that no adjacent parts have the same color. - _Milan Janjic_, Nov 17 2011
%H T. D. Noe, <a href="/A009968/b009968.txt">Table of n, a(n) for n = 0..100</a>
%H Milan Janjic, <a href="http://www.pmfbl.org/janjic/">Enumerative Formulas for Some Functions on Finite Sets</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 (24).
%F G.f.: 1/(1 - 24*x). - _Philippe Deléham_, Nov 23 2008
%F E.g.f.: exp(24x). - _Zerinvary Lajos_, Apr 29 2009
%F a(n) = 24^n; a(n) = 24*a(n-1) for n > 0, a(0) = 1. - _Vincenzo Librandi_, Nov 21 2010
%F a(n) = det(|s(i + 4, j)|, 1 <= i, j <= n), where s(n, k) are Stirling numbers of the first kind. - _Mircea Merca_, Apr 04 2013
%t NestList[24#&, 1, 20] (* _Harvey P. Dale_, Feb 04 2017 *)
%o (Sage) [lucas_number1(n,24,0) for n in range(1, 17)]# - _Zerinvary Lajos_, Apr 29 2009
%o (Magma)[24^n: n in [0..100]] - _Vincenzo Librandi_, Nov 21 2010
%o (PARI) a(n)=24^n \\ _Charles R Greathouse IV_, Sep 24 2015
%o (Scala) LazyList.iterate(1: BigInt)(_ * 24).take(24).toList // _Alonso del Arte_, Apr 24 2020
%o (Python) [24**n for n in range(21)] # _Michael S. Branicky_, Jan 24 2021
%Y Column k = 4 of A225816.
%K nonn,easy
%O 0,2
%A _N. J. A. Sloane_