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 A212596 Number of cards required to build a Menger sponge of level n in origami. 3
 12, 192, 3456, 66048, 1296384, 25731072, 513048576, 10248388608, 204867108864, 4096536870912, 81924294967296, 1638434359738368, 32768274877906944, 655362199023255552, 13107217592186044416, 262144140737488355328, 5242881125899906842624 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS CTRL Byte, 2010-04-13, Menger Sponge Construction ELJJDX, Choux romanesco, vache qui rit et intégrales curvilignes, Am-stram-gram, ticket-ticket-bus-et-tram (French) Nick Hamblet, Σidiot's Blog, 2009-03-01, Counting Cards Michel Lucas, Défi 66 000 tickets (French) Jeannine Mosely, The Institute For Figuring, Business Card Menger Sponge Nicholas Rougeux, Mengermania, Instructions Wikipedia, Menger sponge Index entries for linear recurrences with constant coefficients, signature (28,-160). FORMULA a(n) = 4*(8^n + 2*20^n) = 2^(2*n+3)*5^n+2^(3*n+2). a(n) = A082685(n)*3*4^(n+1). 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 EXAMPLE 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. MAPLE A212596:=n->4*(8^n + 2*20^n); seq(A212596(n), n=0..10); # Wesley Ivan Hurt, Apr 02 2014 MATHEMATICA Table[4 (8^n + 2*20^n), {n, 10}] (* Wesley Ivan Hurt, Apr 02 2014 *) CROSSREFS Sequence in context: A086948 A230539 A230750 * A051620 A144347 A272959 Adjacent sequences:  A212593 A212594 A212595 * A212597 A212598 A212599 KEYWORD easy,nonn AUTHOR Daniel de Rauglaudre, May 22 2012 EXTENSIONS More terms from Colin Barker, Apr 10 2014 STATUS approved

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Last modified January 20 06:37 EST 2019. Contains 319325 sequences. (Running on oeis4.)