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 A009964 Powers of 20. 25
 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 Equivalently, the number of vertices in the n-Menger sponge graph. LINKS T. D. Noe, Table of n, a(n) for n = 0..100 Tanya Khovanova, Recursive Sequences Eric Weisstein's World of Mathematics, Menger Sponge Eric Weisstein's World of Mathematics, Menger Sponge Graph Eric Weisstein's World of Mathematics, Vertex Count Wikipedia, Menger sponge Index entries for linear recurrences with constant coefficients, signature (20). FORMULA G.f.: 1/(1-20*x). E.g.f.: exp(20*x). a(n) = A159991(n)/A000244(n). - Reinhard Zumkeller, May 02 2009 From Vincenzo Librandi, Nov 21 2010: (Start) a(n) = 20^n. a(n) = 20*a(n-1) for n > 0, a(0) = 1. (End) a(n) = A000079(n)*A011557(n) = A000302(n)*A000351(n). - Felix Fröhlich, Jul 09 2016 MAPLE [20^n\$n=0..20]; # Muniru A Asiru, Nov 21 2018 MATHEMATICA 20^Range[0, 10] (* or *) LinearRecurrence[{20}, {1}, 20] (* Eric W. Weisstein, Aug 17 2017 *) PROG (Sage) [20^n for n in xrange(17)] # Zerinvary Lajos, Apr 29 2009 (MAGMA) [20^n: n in [0..100]] // Vincenzo Librandi, Nov 21 2010 (Maxima) makelist(20^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 (GAP) List([0..20], n->20^n); # Muniru A Asiru, Nov 21 2018 (Python) for n in range(0, 20): print(20**n, end=', ') # Stefano Spezia, Nov 21 2018 CROSSREFS Cf. A291066 (edge count). Cf. A000079, A011557; A000302, A000351; A000244, A159991. Sequence in context: A224019 A171294 A267793 * A285874 A007577 A048987 Adjacent sequences:  A009961 A009962 A009963 * A009965 A009966 A009967 KEYWORD nonn,easy AUTHOR STATUS approved

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Last modified October 21 03:24 EDT 2019. Contains 328291 sequences. (Running on oeis4.)