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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
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| 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 R. Janjic (agnus(AT)blic.net), 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
| T. D. Noe, Table of n, a(n) for n=0..100
Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
Tanya Khovanova, Recursive Sequences
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FORMULA
| G.f.: 1/(1-24*x). [From Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Nov 23 2008]
E.g.f.: exp(24x) . [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 29 2009]
a(n)=24^n; a(n)=24*a(n-1) n>0 a(0)=1 [From Vincenzo Librandi, Nov 21 2010]
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PROG
| (Other) sage: [lucas_number1(n, 24, 0) for n in xrange(1, 17)]# [From Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 29 2009]
(MAGMA)[24^n: n in [0..100]] [From Vincenzo Librandi, Nov 21 2010]
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CROSSREFS
| Sequence in context: A188750 A188870 A171298 * A041265 A042106 A158637
Adjacent sequences: A009965 A009966 A009967 * A009969 A009970 A009971
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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