A393907 Number of planar embedding isomorphism classes of the n-Hanoi graph.

1, 2, 10, 60, 408, 2992, 22880, 178880, 1414528, 11250432, 89740800, 716876800, 5730818048, 45829763072, 366570987520, 2932299448320, 23457321811968, 187654279462912, 1501217055703040, 12009667725885440, 96077066928652288, 768615435916541952, 6148919089283727360

Offset

1,2

Comments

These counts allow the mirror image as an isomorphism.

Links

Andrew Howroyd, Table of n, a(n) for n = 1..500

Eric Weisstein's World of Mathematics, Hanoi Graph.

Eric Weisstein's World of Mathematics, Planar Embedding.

Index entries for linear recurrences with constant coefficients, signature (14,-56,64).

Formula

From Andrew Howroyd, Mar 02 2026: (Start)

a(n) = (8^(n-1) + 2*2^(n-1) + 3*4^(n-1))/12 for n > 1.

G.f.: x*(1 - 12*x + 38*x^2 - 32*x^3)/((1 - 2*x)*(1 - 4*x)*(1 - 8*x)). (End)

Mathematica

A393907[n_] := If[n == 1, 1, 2^(n-5)*(2^n+2)*(2^n+4)/3]; Array[A393907, 25] (* or *)
LinearRecurrence[{14, -56, 64}, {1, 2, 10, 60}, 25] (* Paolo Xausa, Mar 03 2026 *)

Prog

(PARI) a(n) = if(n==1, 1, (8^(n-1) + 2*2^(n-1) + 3*4^(n-1))/12) \\ Andrew Howroyd, Mar 02 2026

Crossrefs

Sequence in context: A276310 A372578 A098616 * A082042 A260657 A079856

Adjacent sequences: A393904 A393905 A393906 * A393908 A393909 A393910

Keyword

nonn,easy

Author

Eric W. Weisstein, Mar 02 2026

Extensions

a(5) onward from Andrew Howroyd, Mar 02 2026

Status

approved