cp's OEIS Frontend

A271939 Number of edges in the n-th order Sierpinski carpet graph.

%I A271939 #37 Feb 16 2025 08:33:33
%S A271939 8,88,776,6424,52040,418264,3351944,26833048,214716872,1717892440,
%T A271939 13743611912,109950312472,879606751304,7036866765016,56294972383880,
%U A271939 450359893862296,3602879495272136,28823036995298392,230584299061751048,1844674401792100120
%N A271939 Number of edges in the n-th order Sierpinski carpet graph.
%C A271939 Also the number of maximal and maximum cliques in the n-Sierpinski carpet graph. - _Eric W. Weisstein_, Dec 01 2017
%H A271939 Allan Bickle, <a href="https://allanbickle.files.wordpress.com/2016/05/mengerspongedegree.pdf">Degrees of Menger and Sierpinski Graphs</a>, Congr. Num. 227 (2016) 197-208.
%H A271939 Allan Bickle, <a href="https://allanbickle.files.wordpress.com/2016/05/mengerspongeshort.pdf">MegaMenger Graphs</a>, The College Mathematics Journal, 49 1 (2018) 20-26.
%H A271939 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/EdgeCount.html">Edge Count</a>
%H A271939 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximalClique.html">Maximal Clique</a>
%H A271939 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/MaximumClique.html">Maximum Clique</a>
%H A271939 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SierpinskiCarpetGraph.html">Sierpiński Carpet Graph</a>
%H A271939 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (11,-24).
%F A271939 a(n) = 8 * (8^n - 3^n)/5.
%F A271939 a(n) = 8 * A016140(n).
%F A271939 G.f.: 8*x / ( (8*x-1)*(3*x-1) ). - _R. J. Mathar_, Apr 17 2016
%F A271939 a(n) = 8*a(n-1) + 8*3^(n-1). - _Allan Bickle_, Nov 27 2022
%e A271939 For n=1, the 1st-order Sierpinski carpet graph is an 8-cycle.
%p A271939 seq((1/5)*(8*(8^n-3^n)), n = 1 .. 20);
%t A271939 Table[8 (8^n - 3^n)/5, {n, 20}] (* _Eric W. Weisstein_, Jun 17 2017 *)
%t A271939 LinearRecurrence[{11, -24}, {8, 88}, 20] (* _Eric W. Weisstein_, Jun 17 2017 *)
%t A271939 CoefficientList[Series[8/(1 - 11 x + 24 x^2), {x, 0, 20}], x] (* _Eric W. Weisstein_, Jun 17 2017 *)
%o A271939 (PARI) x='x+O('x^99); Vec(8/((1-3*x)*(1-8*x))) \\ _Altug Alkan_, Apr 17 2016
%Y A271939 Cf. A016140.
%Y A271939 Cf. A001018 (number of vertices in the n-Sierpinski carpet graph).
%K A271939 nonn,easy
%O A271939 1,1
%A A271939 _Emeric Deutsch_, Apr 17 2016