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A009968
Powers of 24: a(n) = 24^n.
25
1, 24, 576, 13824, 331776, 7962624, 191102976, 4586471424, 110075314176, 2641807540224, 63403380965376, 1521681143169024, 36520347436056576, 876488338465357824, 21035720123168587776, 504857282956046106624, 12116574790945106558976, 290797794982682557415424, 6979147079584381377970176, 167499529910025153071284224, 4019988717840603673710821376
OFFSET
0,2
COMMENTS
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.
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
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
FORMULA
G.f.: 1/(1 - 24*x). - Philippe Deléham, Nov 23 2008
E.g.f.: exp(24x). - Zerinvary Lajos, Apr 29 2009
a(n) = 24^n; a(n) = 24*a(n-1) for n > 0, a(0) = 1. - Vincenzo Librandi, Nov 21 2010
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
MATHEMATICA
NestList[24#&, 1, 20] (* Harvey P. Dale, Feb 04 2017 *)
PROG
(Sage) [lucas_number1(n, 24, 0) for n in range(1, 17)]# - Zerinvary Lajos, Apr 29 2009
(Magma)[24^n: n in [0..100]] - Vincenzo Librandi, Nov 21 2010
(PARI) a(n)=24^n \\ Charles R Greathouse IV, Sep 24 2015
(Scala) LazyList.iterate(1: BigInt)(_ * 24).take(24).toList // Alonso del Arte, Apr 24 2020
(Python) [24**n for n in range(21)] # Michael S. Branicky, Jan 24 2021
CROSSREFS
Column k = 4 of A225816.
Sequence in context: A188870 A171298 A268027 * A041265 A042106 A158637
KEYWORD
nonn,easy
STATUS
approved