A246959 Numbers of (undirected) Hamiltonian cycles in the n-Sierpiński gasket graph.
1, 1, 8, 13824, 71328803586048, 9798477119793909670551703700100284084649984
Offset: 1
Keywords
Links
- R. M. Bradley, Statistical mechanics of the travelling salesman on the Sierpinski gasket, J. Physique, 47 (1986), 9-14. doi:10.1051/jphys:019860047010900.
- S.-C. Chang, L.-C. Chen. Hamiltonian walks on the Sierpinski gasket, J. Math. Phys. 52 (2011), 023301. doi:10.1063/1.3545358. arXiv:0909.5541.
- Eric Weisstein's World of Mathematics, Hamiltonian Cycle.
- Eric Weisstein's World of Mathematics, Sierpiński Gasket Graph.
Programs
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Magma
[1,1] cat [Floor(8 * 12^((3^(n-2)-3)/2)): n in [3..10]]; // Vincenzo Librandi, Jun 15 2015
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Mathematica
Join[{1, 1}, Table[8 12^((3^(n - 2) - 3)/2), {n, 3, 8}]] (* Eric W. Weisstein, Jun 17 2017 *) Join[{1, 1}, RecurrenceTable[{a[3] == 8, a[n] == (3 a[n - 1])^3}, a, {n, 3, 8}]] (* Eric W. Weisstein, Mar 25 2018 *)
Formula
For n >= 3, a(n) = 8 * 12^((3^(n-2)-3)/2).
For n >= 4, a(n) = (3*a(n-1))^3.
Comments