OFFSET
1,2
COMMENTS
The level 0 Sierpinski carpet graph is a single vertex. The level n Sierpinski carpet graph is formed from 8 copies of level n-1 by joining boundary vertices between adjacent copies.
LINKS
Paolo Xausa, Table of n, a(n) for n = 1..1000
Allan Bickle, Degrees of Menger and Sierpinski Graphs, Congr. Num. 227 (2016) 197-208.
Allan Bickle, MegaMenger Graphs, The College Mathematics Journal, 49 1 (2018) 20-26.
Eric Weisstein's World of Mathematics, SierpiĆski Carpet Graph
Index entries for linear recurrences with constant coefficients, signature (12,-35,24).
FORMULA
EXAMPLE
The level 1 Sierpinski carpet graph is an 8-cycle, which has 8 degree 2 vertices and 0 degree 3 or 4 vertices. Thus a(1) = 0.
MATHEMATICA
LinearRecurrence[{12, -35, 24}, {0, 4, 100}, 30] (* Paolo Xausa, Oct 16 2023 *)
PROG
(Python)
def A365608(n): return ((3<<3*n-1)-(3**(n-1)<<5))//5+4 # Chai Wah Wu, Nov 27 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Allan Bickle, Sep 12 2023
STATUS
approved