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A212596 Number of cards required to build a Menger sponge of level n in origami. 2


%S 12,192,3456,66048,1296384,25731072,513048576,10248388608,

%T 204867108864,4096536870912,81924294967296,1638434359738368,

%U 32768274877906944,655362199023255552,13107217592186044416,262144140737488355328,5242881125899906842624

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

%H CTRL Byte, 2010-04-13, <a href="http://ctrlbyte.wordpress.com/2010/04/13/2010-04-13-mengersponge/">Menger Sponge Construction</a>

%H 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 Nick Hamblet, Σidiot's Blog, 2009-03-01, <a href="http://sumidiot.wordpress.com/tag/menger-sponge/">Counting Cards</a>

%H Michel Lucas, <a href="http://www.defi66000.fr/">Défi 66 000 tickets (French)</a>

%H Jeannine Mosely, The Institute For Figuring, <a href="http://theiff.org/oexhibits/menger02.html">Business Card Menger Sponge</a>

%H Nicholas Rougeux, Mengermania, <a href="http://c82.net/mengermania/instructions.php">Instructions</a>

%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Menger_sponge">Menger sponge</a>

%H <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (28,-160).

%F a(n) = 4*(8^n + 2*20^n) = 2^(2*n+3)*5^n+2^(3*n+2).

%F a(n) = A082685(n)*3*4^(n+1).

%F a(n) = 28*a(n-1)-160*a(n-2). G.f.: -12*(12*x-1) / ((8*x-1)*(20*x-1)). - _Colin Barker_, Apr 10 2014

%e 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:=n->4*(8^n + 2*20^n); seq(A212596(n), n=0..10); # _Wesley Ivan Hurt_, Apr 02 2014

%t Table[4 (8^n + 2*20^n), {n, 10}] (* _Wesley Ivan Hurt_, Apr 02 2014 *)

%K easy,nonn

%O 0,1

%A _Daniel de Rauglaudre_, May 22 2012

%E More terms from _Colin Barker_, Apr 10 2014

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Last modified August 17 22:32 EDT 2018. Contains 313817 sequences. (Running on oeis4.)