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

12, 192, 3456, 66048, 1296384, 25731072, 513048576, 10248388608, 204867108864, 4096536870912, 81924294967296, 1638434359738368, 32768274877906944, 655362199023255552, 13107217592186044416, 262144140737488355328, 5242881125899906842624

Offset

0,1

Links

Table of n, a(n) for n=0..16.

CTRL Byte, 2010-04-13, Menger Sponge Construction [broken link]

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).

From Colin Barker, Apr 10 2014: (Start)

a(n) = 28*a(n-1)-160*a(n-2).

G.f.: -12*(12*x-1) / ((8*x-1)*(20*x-1)). (End)

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

Cf. A082685.

Sequence in context: A230539 A230750 A358367 * A051620 A144347 A359453

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