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A212596
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Number of cards required to build a Menger sponge of level n in origami.
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0
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12, 192, 3456, 66048, 1296384, 25731072, 513048576, 10248388608, 204867108864, 4096536870912, 81924294967296, 1638434359738368, 32768274877906944, 655362199023255552
(list;
graph;
refs;
listen;
history;
text;
internal format)
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OFFSET
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0,1
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LINKS
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Table of n, a(n) for n=0..13.
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)
Dr. Jeannine Mosely, The Institute For Figuring, Business Card Menger Sponge
Nicholas Rougeux, Mengermania, Instructions
Wikipedia, Menger sponge
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FORMULA
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a(n) = 4*(8^n + 2*20^n) = 2^(2*n+3)*5^n+2^(3*n+2)
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EXAMPLE
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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.
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CROSSREFS
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Equal to A082685*3*4^(n+1)
Sequence in context: A196483 A196716 A086948 * A051620 A144347 A095351
Adjacent sequences: A212593 A212594 A212595 * A212597 A212598 A212599
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KEYWORD
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easy,nonn
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AUTHOR
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Daniel de Rauglaudre, May 22 2012
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STATUS
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approved
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