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1, 20, 400, 8000, 160000, 3200000, 64000000, 1280000000, 25600000000, 512000000000, 10240000000000, 204800000000000, 4096000000000000, 81920000000000000, 1638400000000000000, 32768000000000000000
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,2
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COMMENTS
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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 20-colored compositions of n such that no adjacent parts have the same color. - Milan Janjic, Nov 17 2011
a(n) gives the number of small cubes in the n-th iteration of the Menger sponge fractal. - Felix Fröhlich, Jul 09 2016
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LINKS
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T. D. Noe, Table of n, a(n) for n = 0..100
Tanya Khovanova, Recursive Sequences
Wikipedia, Menger sponge
Index entries for linear recurrences with constant coefficients, signature (20).
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FORMULA
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G.f.: 1/(1-20x), e.g.f.: exp(20x)
a(n) = A159991(n)/A000244(n). - Reinhard Zumkeller, May 02 2009
a(n) = 20^n; a(n) = 20*a(n-1) n>0 a(0)=1. - Vincenzo Librandi, Nov 21 2010
a(n) = A000079(n)*A011557(n) = A000302(n)*A000351(n). - Felix Fröhlich, Jul 09 2016
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PROG
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(Sage) [lucas_number1(n, 20, 0) for n in xrange(1, 17)] # Zerinvary Lajos, Apr 29 2009
(MAGMA)[20^n: n in [0..100]] // Vincenzo Librandi, Nov 21 2010
(Maxima) A009964(n):=20^n$
makelist(A009964(n), n, 0, 30); /* Martin Ettl, Nov 05 2012 */
(PARI) a(n)=20^n \\ Charles R Greathouse IV, Jun 19 2015
(PARI) powers(20, 12) \\ Charles R Greathouse IV, Jun 19 2015
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CROSSREFS
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Sequence in context: A224019 A171294 A267793 * A285874 A007577 A048987
Adjacent sequences: A009961 A009962 A009963 * A009965 A009966 A009967
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane.
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STATUS
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approved
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