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A009964 Powers of 20. 18
1, 20, 400, 8000, 160000, 3200000, 64000000, 1280000000, 25600000000, 512000000000, 10240000000000, 204800000000000, 4096000000000000, 81920000000000000, 1638400000000000000, 32768000000000000000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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

LINKS

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).

FORMULA

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

PROG

(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

CROSSREFS

Sequence in context: A224019 A171294 A267793 * A285874 A007577 A048987

Adjacent sequences:  A009961 A009962 A009963 * A009965 A009966 A009967

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified June 25 18:15 EDT 2017. Contains 288729 sequences.