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 A375256 #21 Sep 23 2024 08:07:18
%S A375256 3,12,39,129,453,1677,6429,25149,99453,395517,1577469,6300669,
%T A375256 25184253,100700157,402726909,1610760189,6442745853,25770393597,
%U A375256 103080394749,412319219709,1649272160253,6597079203837,26388297940989,105553154015229,422212540563453,1688850011258877,6755399743045629
%N A375256 Number of pairs of antipodal vertices in the level n Hanoi graph.
%C A375256 A level 1 Hanoi graph is a triangle. Level n+1 is formed from three copies of level n by adding edges between pairs of corner vertices of each pair of triangles. This graph represents the allowable moves in the Towers of Hanoi problem with n disks.
%C A375256 Antipodal vertices are a pair of vertices at maximum distance in a graph. The diameter of the level n Hanoi graph is 2^n - 1.
%H A375256 Paolo Xausa, <a href="/A375256/b375256.txt">Table of n, a(n) for n = 1..1000</a>
%H A375256 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 A375256 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 A375256 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/HanoiGraph.html">Hanoi Graph</a>
%H A375256 <a href="/index/Rec#order_03">Index entries for linear recurrences with constant coefficients</a>, signature (7,-14,8).
%F A375256 a(n) = 3*(2^(2n-3)+3*2^(n-2)-1).
%F A375256 a(n) = A370933(n+1) - 3.
%F A375256 a(n) = 3*A297928(n-2) for n>=2. - _Alois P. Heinz_, Sep 23 2024
%e A375256 2 example graphs:
%e A375256 o
%e A375256 / \
%e A375256 o---o
%e A375256 / \
%e A375256 o o o
%e A375256 / \ / \ / \
%e A375256 o---o o---o---o---o
%e A375256 Graph: H_1 H_2
%e A375256 Since the level 1 Hanoi graph is a triangle, a(1) = 3.
%t A375256 A375256[n_] := 3*(2^(2*n - 3) + 3*2^(n - 2) - 1);
%t A375256 Array[A375256, 30] (* or *)
%t A375256 LinearRecurrence[{7, -14, 8}, {3, 12, 39}, 30] (* _Paolo Xausa_, Sep 23 2024 *)
%o A375256 (PARI) a(n) = 3*(2^(2*n-3)+3*2^(n-2)-1); \\ _Michel Marcus_, Aug 08 2024
%Y A375256 Cf. A000225, A029858, A058809 (Hanoi graphs).
%Y A375256 Cf. A370933 (antipodal pairs in Sierpiński triangle graphs).
%Y A375256 Cf. A193233, A297928.
%K A375256 nonn
%O A375256 1,1
%A A375256 _Allan Bickle_, Aug 07 2024
%E A375256 More terms from _Michel Marcus_, Aug 08 2024