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).
From Vincenzo Librandi, Nov 21 2010: (Start)
a(n) = 20^n.
a(n) = 20*a(n-1) for n > 0, a(0) = 1. (End)
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).
KEYWORD
nonn,easy
AUTHOR
STATUS
approved