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A212596 Number of cards required to build a Menger sponge of level n in origami. 0
12, 192, 3456, 66048, 1296384, 25731072, 513048576, 10248388608, 204867108864, 4096536870912, 81924294967296, 1638434359738368, 32768274877906944, 655362199023255552 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

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

FORMULA

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

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.

CROSSREFS

Equal to A082685*3*4^(n+1)

Sequence in context: A086948 A230539 A230750 * A051620 A144347 A095351

Adjacent sequences:  A212593 A212594 A212595 * A212597 A212598 A212599

KEYWORD

easy,nonn

AUTHOR

Daniel de Rauglaudre, May 22 2012

STATUS

approved

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Last modified April 18 23:13 EDT 2014. Contains 240735 sequences.