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 A370933 #26 Sep 23 2024 11:32:10
%S A370933 6,15,42,132,456,1680,6432,25152,99456,395520,1577472,6300672,
%T A370933 25184256,100700160,402726912,1610760192,6442745856,25770393600,
%U A370933 103080394752,412319219712,1649272160256,6597079203840,26388297940992,105553154015232,422212540563456,1688850011258880,6755399743045632
%N A370933 Number of pairs of antipodal vertices in the level n>1 Sierpiński triangle graph.
%C A370933 A level 1 Sierpiński triangle graph is a triangle. Level n+1 is formed from three copies of level n by identifying pairs of corner vertices of each pair of triangles.
%C A370933 Antipodal vertices are a pair of vertices at maximum distance in a graph. The diameter of the level n Sierpiński triangle graph is 2^(n-1).
%H A370933 Paolo Xausa, <a href="/A370933/b370933.txt">Table of n, a(n) for n = 2..1000</a>
%H A370933 <a href="/index/Rec#order_02">Index entries for linear recurrences with constant coefficients</a>, signature (6,-8).
%H A370933 Allan Bickle, <a href="https://allanbickle.wordpress.com/wp-content/uploads/2016/05/sierpinskigraphpaper2.pdf">Properties of Sierpinski Triangle Graphs</a>, Springer PROMS 448 (2021) 295-303.
%H A370933 A. Hinz, S. Klavzar, and S. Zemljic, <a href="https://doi.org/10.1016/j.dam.2016.09.024">A survey and classification of Sierpinski-type graphs</a>, Discrete Applied Mathematics 217 3 (2017), 565-600.
%H A370933 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/SierpinskiGasketGraph.html">Sierpiński Gasket Graph</a>
%F A370933 a(n) = 3*2^(n-3)*(2^(n-2)+3).
%F A370933 a(n) = 3*A257273(n-2).
%F A370933 a(n) = A375256(n-1) + 3.
%e A370933 3 example graphs: o
%e A370933 / \
%e A370933 o---o
%e A370933 / \ / \
%e A370933 o o---o---o
%e A370933 / \ / \ / \
%e A370933 o o---o o---o o---o
%e A370933 / \ / \ / \ / \ / \ / \ / \
%e A370933 o---o o---o---o o---o---o---o---o
%e A370933 Graph: S_1 S_2 S_3
%e A370933 For S_2, there are 3 pairs of corners and 3 pairs of a corner and a middle vertex, so a(2) = 6.
%t A370933 A370933[n_] := 3*2^(n - 3)*(2^(n - 2) + 3);
%t A370933 Array[A370933, 30, 2] (* or *)
%t A370933 LinearRecurrence[{6, -8}, {6, 15}, 30] (* _Paolo Xausa_, Sep 23 2024 *)
%o A370933 (PARI) a(n) = 3*2^(n-3)*(2^(n-2)+3); \\ _Michel Marcus_, Aug 08 2024
%Y A370933 Cf. A007283, A029858, A067771, A193277, A233774, A233775, A246959, A298202 (Sierpiński triangle graphs).
%Y A370933 Cf. A375256 (antipodal pairs in Hanoi graphs).
%K A370933 nonn,easy
%O A370933 2,1
%A A370933 _Allan Bickle_, Aug 07 2024
%E A370933 More terms from _Michel Marcus_, Aug 08 2024