%I #32 Dec 30 2023 13:25:38

%S 1,1,8,13824,71328803586048,

%T 9798477119793909670551703700100284084649984

%N Numbers of (undirected) Hamiltonian cycles in the n-Sierpiński gasket graph.

%H R. M. Bradley, <a href="https://hal.archives-ouvertes.fr/jpa-00210189/">Statistical mechanics of the travelling salesman on the Sierpinski gasket</a>, J. Physique, 47 (1986), 9-14. doi:<a href="http://dx.doi.org/10.1051/jphys:019860047010900">10.1051/jphys:019860047010900</a>.

%H S.-C. Chang, L.-C. Chen. Hamiltonian walks on the Sierpinski gasket, J. Math. Phys. 52 (2011), 023301. doi:<a href="http://dx.doi.org/10.1063/1.3545358">10.1063/1.3545358</a>. arXiv:<a href="http://arxiv.org/abs/0909.5541">0909.5541</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/HamiltonianCycle.html">Hamiltonian Cycle</a>.

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/SierpinskiGasketGraph.html">Sierpiński Gasket Graph</a>.

%F For n >= 3, a(n) = 8 * 12^((3^(n-2)-3)/2).

%F For n >= 4, a(n) = (3*a(n-1))^3.

%t Join[{1, 1}, Table[8 12^((3^(n - 2) - 3)/2], {n, 8}]] (* _Eric W. Weisstein_, Jun 17 2017 *)

%t Join[{1, 1}, RecurrenceTable[{a[3] == 8, a[n] == (3 a[n - 1])^3}, a, {n, 3, 8}]] (* _Eric W. Weisstein_, Mar 25 2018 *)

%o (Magma) [1,1] cat [Floor(8 * 12^((3^(n-2)-3)/2)): n in [3..10]]; // _Vincenzo Librandi_, Jun 15 2015

%Y Cf. A234635, A246957, A246958.

%K nonn

%O 1,3

%A _Max Alekseyev_, Sep 08 2014