This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A302507 #13 Feb 16 2025 08:33:53
%S A302507 0,8,32,104,320,968,2912,8744,26240,78728,236192,708584,2125760,
%T A302507 6377288,19131872,57395624,172186880,516560648,1549681952,4649045864,
%U A302507 13947137600,41841412808,125524238432,376572715304,1129718145920,3389154437768,10167463313312
%N A302507 a(n) = 4*(3^n-1).
%C A302507 Triameter of the n-Sierpinski carpet graph.
%C A302507 Binomial transform is 0,8,48,224,960,... A211012 shifted. - _R. J. Mathar_, Apr 07 2022
%H A302507 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/GraphTriameter.html">Graph Triameter</a>
%H A302507 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SierpinskiCarpetGraph.html">Sierpinski Carpet Graph</a>
%H A302507 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (4,-3).
%F A302507 a(n) = 4*A024023(n).
%F A302507 a(n) = 4*a(n-1) - 3*a(n-2).
%F A302507 G.f.: 8*x/((1 - x)*(1 - 3*x)).
%F A302507 a(n) = 8*A003462(n). - _R. J. Mathar_, Apr 07 2022
%t A302507 Table[4 (3^n - 1), {n, 0, 20}]
%t A302507 4 (3^Range[0, 20] - 1)
%t A302507 LinearRecurrence[{4, -3}, {8, 32}, {0, 20}]
%t A302507 CoefficientList[Series[8 x/((1 - x) (1 - 3 x)), {x, 0, 20}], x]
%o A302507 (PARI) for(n=0,30, print1(4*(3^n-1), ", ")) \\ _G. C. Greubel_, Apr 09 2018
%o A302507 (Magma) [4*(3^n -1): n in [0..30]]; // _G. C. Greubel_, Apr 09 2018
%Y A302507 Cf. A024023.
%K A302507 nonn,easy
%O A302507 0,2
%A A302507 _Eric W. Weisstein_, Apr 09 2018