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A009968 Powers of 24: a(n) = 24^n. 17
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; text; internal format)
OFFSET

0,2

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 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

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

Index entries for linear recurrences with constant coefficients, signature (24).

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 xrange(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

CROSSREFS

Column k=4 of A225816.

Sequence in context: A188870 A171298 A268027 * A041265 A042106 A158637

Adjacent sequences:  A009965 A009966 A009967 * A009969 A009970 A009971

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified March 29 15:31 EDT 2017. Contains 284273 sequences.