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A009968
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Powers of 24: a(n) = 24^n.
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25
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1, 24, 576, 13824, 331776, 7962624, 191102976, 4586471424, 110075314176, 2641807540224, 63403380965376, 1521681143169024, 36520347436056576, 876488338465357824, 21035720123168587776, 504857282956046106624, 12116574790945106558976, 290797794982682557415424, 6979147079584381377970176, 167499529910025153071284224, 4019988717840603673710821376
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OFFSET
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0,2
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COMMENTS
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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
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LINKS
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FORMULA
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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
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MATHEMATICA
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PROG
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(Sage) [lucas_number1(n, 24, 0) for n in range(1, 17)]# - Zerinvary Lajos, Apr 29 2009
(Scala) LazyList.iterate(1: BigInt)(_ * 24).take(24).toList // Alonso del Arte, Apr 24 2020
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CROSSREFS
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KEYWORD
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nonn,easy
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AUTHOR
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STATUS
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approved
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