The On-Line Encyclopedia of Integer Sequences (OEIS)

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A246959

Numbers of (undirected) Hamiltonian cycles in the n-Sierpiński gasket graph.
(history; published version)

#32 by Peter Luschny at Sat Dec 30 13:25:38 EST 2023

STATUS

proposed

approved

#31 by Jon E. Schoenfield at Sat Dec 30 13:21:24 EST 2023

STATUS

editing

proposed

#30 by Jon E. Schoenfield at Sat Dec 30 13:21:14 EST 2023

LINKS

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>.

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>.

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

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

FORMULA

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

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

STATUS

approved

editing

#29 by Michael De Vlieger at Sat Dec 09 09:00:25 EST 2023

STATUS

proposed

approved

#28 by Eric W. Weisstein at Sat Dec 09 08:01:27 EST 2023

STATUS

editing

proposed

#27 by Eric W. Weisstein at Sat Dec 09 08:01:19 EST 2023

NAME

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

LINKS

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

STATUS

approved

editing

#26 by Charles R Greathouse IV at Thu Sep 08 08:46:09 EDT 2022

PROG

(MAGMAMagma) [1, 1] cat [Floor(8 * 12^((3^(n-2)-3)/2)): n in [3..10]]; // Vincenzo Librandi, Jun 15 2015

Discussion

Thu Sep 08

08:46

OEIS Server: https://oeis.org/edit/global/2944

#25 by Susanna Cuyler at Mon Mar 26 19:58:55 EDT 2018

STATUS

proposed

approved

#24 by Michel Marcus at Sun Mar 25 11:41:57 EDT 2018

STATUS

editing

proposed

#23 by Michel Marcus at Sun Mar 25 11:41:52 EDT 2018

LINKS

R. M. Bradley, <a href="httphttps://hal.archives-ouvertes.fr/docs/00/21/01/89/PDF/ajpjpa-jphys_1986_47_1_9_0.pdf00210189/">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>

STATUS

proposed

editing