A304960 Number of business cards required to build an origami level n Mosely snowflake sponge.

12, 168, 2784, 48912, 874416, 15709488, 282620784, 5086424112, 91551884016, 1647915162288, 29662379171184, 533922356331312, 9610600070213616, 172990789545095088, 3113834153217961584, 56049014464954558512, 1008882258904338303216, 18159880652953870707888

Offset

0,1

References

Thomas Hull, Project Origami: Activities for Exploring Mathematics, A K Peters/CRC Press, 2006.

Links

Table of n, a(n) for n=0..17.

Franck Ramaharo, Level Two Mosely Snowflake Sponge

Origami Resource Center, Business Card Origami

Origami Resource Center, Mosely Snowflake Sponge Fractal (Level 3)

The Institute For Figuring, The Mosely Snowflake Sponge at the USC Libraries

The Institute For Figuring, USC Sponge Guide

Wikipedia, Mosely snowflake

Index entries for linear recurrences with constant coefficients, signature (23,-90)

Formula

a(n) = (108*18^n + 48*5^n)/13.

a(n) = 18*a(n-1) - 48*5^(n - 1);

a(n) = 23*a(n-1) - 90*a(n-2), with a(0) = 12 and a(1) = 168.

G.f.: - 12*(9*x - 1)/((5*x - 1)*(18*x - 1)).

E.g.f.: (108*exp(18*x) + 48*exp(5*x))/13.

Example

a(1) = 168 because 108 business cards are needed for the squeleton and 60 more for the panels (see guide in links).

Maple

seq((108*18^n + 48*5^n)/13, n = 0 .. 50);

Mathematica

LinearRecurrence[{23, -90}, {12, 168}, 50]

Prog

(Maxima) makelist((108*18^n + 48*5^n)/13, n, 0, 50);

Crossrefs

Cf. A212596 (Origami Menger sponge).

Sequence in context: A216702 A320761 A282045 * A113380 A071103 A012489

Adjacent sequences: A304957 A304958 A304959 * A304961 A304962 A304963

Keyword

nonn,easy

Author

Franck Maminirina Ramaharo, May 22 2018

Status

approved