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A212596 Number of cards required to build a Menger sponge of level n in origami.

%I A212596 #36 Jul 30 2020 17:12:23
%S A212596 12,192,3456,66048,1296384,25731072,513048576,10248388608,
%T A212596 204867108864,4096536870912,81924294967296,1638434359738368,
%U A212596 32768274877906944,655362199023255552,13107217592186044416,262144140737488355328,5242881125899906842624
%N A212596 Number of cards required to build a Menger sponge of level n in origami.
%H A212596 CTRL Byte, 2010-04-13, <a href="http://ctrlbyte.wordpress.com/2010/04/13/2010-04-13-mengersponge/">Menger Sponge Construction</a> [broken link]
%H A212596 ELJJDX, Choux romanesco, vache qui rit et intégrales curvilignes, <a href="http://eljjdx.canalblog.com/archives/2009/12/20/16221444.html">Am-stram-gram, ticket-ticket-bus-et-tram (French)</a>
%H A212596 Nick Hamblet, Σidiot's Blog, 2009-03-01, <a href="http://sumidiot.wordpress.com/tag/menger-sponge/">Counting Cards</a>
%H A212596 Michel Lucas, <a href="http://www.defi66000.fr/">Défi 66 000 tickets (French)</a>
%H A212596 Jeannine Mosely, The Institute For Figuring, <a href="http://theiff.org/oexhibits/menger02.html">Business Card Menger Sponge</a>
%H A212596 Nicholas Rougeux, Mengermania, <a href="https://web.archive.org/web/20150419135725/http://c82.net/mengermania/instructions.php">Instructions</a>
%H A212596 Wikipedia, <a href="http://en.wikipedia.org/wiki/Menger_sponge">Menger sponge</a>
%H A212596 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (28,-160).
%F A212596 a(n) = 4*(8^n + 2*20^n) = 2^(2*n+3)*5^n+2^(3*n+2).
%F A212596 a(n) = A082685(n)*3*4^(n+1).
%F A212596 From _Colin Barker_, Apr 10 2014: (Start)
%F A212596 a(n) = 28*a(n-1)-160*a(n-2).
%F A212596 G.f.: -12*(12*x-1) / ((8*x-1)*(20*x-1)). (End)
%e A212596 12 cards (a(0)) are required for a single origami cube: 6 for the cube skeleton, and 6 for panels or possible links to other cubes.
%p A212596 A212596:=n->4*(8^n + 2*20^n); seq(A212596(n), n=0..10); # _Wesley Ivan Hurt_, Apr 02 2014
%t A212596 Table[4 (8^n + 2*20^n), {n, 10}] (* _Wesley Ivan Hurt_, Apr 02 2014 *)
%Y A212596 Cf. A082685.
%K A212596 easy,nonn
%O A212596 0,1
%A A212596 _Daniel de Rauglaudre_, May 22 2012
%E A212596 More terms from _Colin Barker_, Apr 10 2014