This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A009964 #80 Feb 16 2025 08:32:32
%S A009964 1,20,400,8000,160000,3200000,64000000,1280000000,25600000000,
%T A009964 512000000000,10240000000000,204800000000000,4096000000000000,
%U A009964 81920000000000000,1638400000000000000,32768000000000000000
%N A009964 Powers of 20.
%C A009964 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.
%C A009964 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
%C A009964 a(n) gives the number of small cubes in the n-th iteration of the Menger sponge fractal. - _Felix Fröhlich_, Jul 09 2016
%C A009964 Equivalently, the number of vertices in the n-Menger sponge graph.
%H A009964 T. D. Noe, <a href="/A009964/b009964.txt">Table of n, a(n) for n = 0..100</a>
%H A009964 Allan Bickle, <a href="https://allanbickle.files.wordpress.com/2016/05/mengerspongedegree.pdf">Degrees of Menger and Sierpinski Graphs</a>, Congr. Num. 227 (2016) 197-208.
%H A009964 Allan Bickle, <a href="https://allanbickle.files.wordpress.com/2016/05/mengerspongeshort.pdf">MegaMenger Graphs</a>, The College Mathematics Journal, 49 1 (2018) 20-26.
%H A009964 Tanya Khovanova, <a href="http://www.tanyakhovanova.com/RecursiveSequences/RecursiveSequences.html">Recursive Sequences</a>
%H A009964 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MengerSponge.html">Menger Sponge</a>
%H A009964 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MengerSpongeGraph.html">Menger Sponge Graph</a>
%H A009964 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/VertexCount.html">Vertex Count</a>
%H A009964 Wikipedia, <a href="https://en.wikipedia.org/wiki/Menger_sponge">Menger sponge</a>
%H A009964 <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (20).
%F A009964 G.f.: 1/(1-20*x).
%F A009964 E.g.f.: exp(20*x).
%F A009964 a(n) = A159991(n)/A000244(n). - _Reinhard Zumkeller_, May 02 2009
%F A009964 From _Vincenzo Librandi_, Nov 21 2010: (Start)
%F A009964 a(n) = 20^n.
%F A009964 a(n) = 20*a(n-1) for n > 0, a(0) = 1. (End)
%F A009964 a(n) = A000079(n)*A011557(n) = A000302(n)*A000351(n). - _Felix Fröhlich_, Jul 09 2016
%p A009964 [20^n$n=0..20]; # _Muniru A Asiru_, Nov 21 2018
%t A009964 20^Range[0, 10] (* or *) LinearRecurrence[{20}, {1}, 20] (* _Eric W. Weisstein_, Aug 17 2017 *)
%o A009964 (Sage) [20^n for n in range(21)] # _Zerinvary Lajos_, Apr 29 2009
%o A009964 (Magma) [20^n: n in [0..100]] // _Vincenzo Librandi_, Nov 21 2010
%o A009964 (Maxima) makelist(20^n,n,0,30); /* _Martin Ettl_, Nov 05 2012 */
%o A009964 (PARI) a(n)=20^n \\ _Charles R Greathouse IV_, Jun 19 2015
%o A009964 (PARI) powers(20,12) \\ _Charles R Greathouse IV_, Jun 19 2015
%o A009964 (GAP) List([0..20],n->20^n); # _Muniru A Asiru_, Nov 21 2018
%o A009964 (Python) [20**n for n in range(21)] # _Stefano Spezia_, Nov 21 2018
%Y A009964 Cf. A291066 (edge count).
%Y A009964 Cf. A000079, A011557; A000302, A000351; A000244, A159991.
%Y A009964 Cf. A291066, A083233, and A332705 on the surface area of the n-Menger sponge graph.
%K A009964 nonn,easy
%O A009964 0,2
%A A009964 _N. J. A. Sloane_