OFFSET
1,1
COMMENTS
Also the number of maximal and maximum cliques in the n-Sierpinski carpet graph. - Eric W. Weisstein, Dec 01 2017
LINKS
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, Edge Count
Eric Weisstein's World of Mathematics, Maximal Clique
Eric Weisstein's World of Mathematics, Maximum Clique
Eric Weisstein's World of Mathematics, SierpiĆski Carpet Graph
Index entries for linear recurrences with constant coefficients, signature (11,-24).
FORMULA
a(n) = 8 * (8^n - 3^n)/5.
a(n) = 8 * A016140(n).
G.f.: 8*x / ( (8*x-1)*(3*x-1) ). - R. J. Mathar, Apr 17 2016
a(n) = 8*a(n-1) + 8*3^(n-1). - Allan Bickle, Nov 27 2022
EXAMPLE
For n=1, the 1st-order Sierpinski carpet graph is an 8-cycle.
MAPLE
seq((1/5)*(8*(8^n-3^n)), n = 1 .. 20);
MATHEMATICA
Table[8 (8^n - 3^n)/5, {n, 20}] (* Eric W. Weisstein, Jun 17 2017 *)
LinearRecurrence[{11, -24}, {8, 88}, 20] (* Eric W. Weisstein, Jun 17 2017 *)
CoefficientList[Series[8/(1 - 11 x + 24 x^2), {x, 0, 20}], x] (* Eric W. Weisstein, Jun 17 2017 *)
PROG
(PARI) x='x+O('x^99); Vec(8/((1-3*x)*(1-8*x))) \\ Altug Alkan, Apr 17 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Emeric Deutsch, Apr 17 2016
STATUS
approved