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

1,1

Comments

Also the number of maximal and maximum cliques in the n-Sierpinski carpet graph. - Eric W. Weisstein, Dec 01 2017

Links

Table of n, a(n) for n=1..20.

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).

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

Cf. A016140.

Cf. A001018 (number of vertices in the n-Sierpinski carpet graph).

Sequence in context: A367278 A030984 A109021 * A043043 A003492 A368919

Adjacent sequences: A271936 A271937 A271938 * A271940 A271941 A271942

Keyword

nonn,easy

Author

Emeric Deutsch, Apr 17 2016

Status

approved