A009964 Powers of 20.

1, 20, 400, 8000, 160000, 3200000, 64000000, 1280000000, 25600000000, 512000000000, 10240000000000, 204800000000000, 4096000000000000, 81920000000000000, 1638400000000000000, 32768000000000000000

Offset

0,2

Comments

Same as Pisot sequences E(1, 20), L(1, 20), P(1, 20), T(1, 20). Essentially same as Pisot sequences E(20, 400), L(20, 400), P(20, 400), T(20, 400). See A008776 for definitions of Pisot sequences.

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

Allan Bickle, Degrees of Menger and Sierpinski Graphs, Congr. Num. 227 (2016) 197-208.

Allan Bickle, MegaMenger Graphs, The College Mathematics Journal, 49 1 (2018) 20-26.

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 range(21)] # 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) [20**n for n in range(21)] # Stefano Spezia, Nov 21 2018

Crossrefs

Cf. A291066 (edge count).

Cf. A000079, A011557; A000302, A000351; A000244, A159991.

Cf. A291066, A083233, and A332705 on the surface area of the n-Menger sponge graph.

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