A375256 Number of pairs of antipodal vertices in the level n Hanoi graph.
3, 12, 39, 129, 453, 1677, 6429, 25149, 99453, 395517, 1577469, 6300669, 25184253, 100700157, 402726909, 1610760189, 6442745853, 25770393597, 103080394749, 412319219709, 1649272160253, 6597079203837, 26388297940989, 105553154015229, 422212540563453, 1688850011258877, 6755399743045629
Offset: 1
Keywords
Examples
2 example graphs:
o
/ \
o---o
/ \
o o o
/ \ / \ / \
o---o o---o---o---o
Graph: H_1 H_2
Since the level 1 Hanoi graph is a triangle, a(1) = 3.
Links
- Paolo Xausa, Table of n, a(n) for n = 1..1000
- Allan Bickle, Properties of Sierpinski Triangle Graphs, Springer PROMS 448 (2021) 295-303.
- A. Hinz, S. Klavzar, and S. Zemljic, A survey and classification of Sierpinski-type graphs, Discrete Applied Mathematics 217 3 (2017), 565-600.
- Eric Weisstein's World of Mathematics, Hanoi Graph
- Index entries for linear recurrences with constant coefficients, signature (7,-14,8).
Crossrefs
Programs
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Mathematica
A375256[n_] := 3*(2^(2*n - 3) + 3*2^(n - 2) - 1); Array[A375256, 30] (* or *) LinearRecurrence[{7, -14, 8}, {3, 12, 39}, 30] (* Paolo Xausa, Sep 23 2024 *)
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PARI
a(n) = 3*(2^(2*n-3)+3*2^(n-2)-1); \\ Michel Marcus, Aug 08 2024
Formula
a(n) = 3*(2^(2n-3)+3*2^(n-2)-1).
a(n) = A370933(n+1) - 3.
a(n) = 3*A297928(n-2) for n>=2. - Alois P. Heinz, Sep 23 2024
Extensions
More terms from Michel Marcus, Aug 08 2024
Comments