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

Author

Franck Maminirina Ramaharo, May 22 2018

Keywords

• nonn
• easy

Examples

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

References

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

Links

• 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)

Crossrefs

Cf. A212596 (Origami Menger sponge).

Programs

Maple

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

Mathematica

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

Maxima

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

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.