OFFSET
0,1
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)
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
KEYWORD
nonn,easy
AUTHOR
Franck Maminirina Ramaharo, May 22 2018
STATUS
approved