A271939 Number of edges in the n-th order Sierpinski carpet graph.
8, 88, 776, 6424, 52040, 418264, 3351944, 26833048, 214716872, 1717892440, 13743611912, 109950312472, 879606751304, 7036866765016, 56294972383880, 450359893862296, 3602879495272136, 28823036995298392, 230584299061751048, 1844674401792100120
Offset: 1
Examples
For n=1, the 1st-order Sierpinski carpet graph is an 8-cycle.
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, Sierpiński Carpet Graph
- Index entries for linear recurrences with constant coefficients, signature (11,-24).
Programs
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Maple
seq((1/5)*(8*(8^n-3^n)), n = 1 .. 20);
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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 *) -
PARI
x='x+O('x^99); Vec(8/((1-3*x)*(1-8*x))) \\ Altug Alkan, Apr 17 2016
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
Comments